Were there often intra-USSR wars? If not, why not?

Holodomor of 1932-33, the Soviet government simply decided to kill the Ukrainians by starvation, taking everything, and closing all borders. All wars in the USSR were resolved by sending all the unwanted to the GULAG. (The Main Directorate of Camps and Places of Detention, emerged in 1930, existed for thirty years, and was liquidated by 1960) The GULAG system in the USSR consisted of 30 thousand places of detention: from the Arctic Circle to Kazakhstan, from the western borders to the Far East. The USSR is a prison power with completely closed borders. The number of prisoners was equal to the number of people living in about two European countries combined, and this does not include prisons. What wars?

There were not too many wars and inter-ethnic conflicts inside of the USSR just because anyone who has dissent thoughts was immediately killed or imprisoned during repression years. Also, there were about 10 kgb agents per 100 citizens. So almost all citizens knew enough to be ok with the regime especially not to have any thoughts about ethnic conflicts. But everyone hates another, that appear after the USSR fall.

It looks like the Soviet Union kept peace by damping out nationalism. Near the end of the cold war, when Gorbachev allowed nationalism, was when the setting for post-Soviet conflicts took root.

[Azerbaijan-Armenia] hatreds are not ancient: The first large-scale ethnic clashes between Armenians and Azerbaijanis took place as late as in 1905, during a period of turmoil born from modernization within the Russian Empire. They are, instead, based on the grievances, and the particular forms of nationalism that emerged after the fall of the Soviet Union. These might have been slightly open to negotiation at that time; they have, by now, crystallized into two identities that are radically incompatible and contradictory, among peoples most of whom have never met anyone from “the other side” in real life.

As a result, the other is routinely de-humanized through a number of hateful stereotypes. To Armenians, Azerbaijanis are “Turks”: nomadic Central Asian intruders into the region engaged in a millennium-long effort to drive them out through massacre and misrule. Inferences are made about a purported “Turkish psychology” prone to such violent behavior; and Azerbaijanis are seen as unsophisticated, and lacking in indigenous culture. Their existence as a real ethnic group before 1918 – the founding of the first independent Azerbaijani republic – is denied. The cultural legacy of their ancestors – like the Blue Mosque in Yerevan, or the mosques in Karabakh – are ascribed to generic “Muslims,” or the long-time imperial rulers over this region – the Persians.

The Azerbaijani version is a variation on these discourses: Armenians are often portrayed as a rootless nation engaged in an ongoing effort at encroachment into the South Caucasus. They are often generalized as inherently “terroristic”; collectively seen as cunning, devious, culturally parasitical, capable of misleading the world through a diaspora whose (hidden) power is often overstated. Their history in the South Caucasus is also dismissed as a myth. One standard account is of Armenians arriving in the area only in the 19th century, with any Armenian monuments in the region identified as “Caucasian Albanian,” a now-extinct Christian culture seen as part of Azerbaijan’s historic lineage.

Source

In other words, it's only at the end of the Soviet Union that Azerbaijan and Armenia saw each other so negatively. Therefore, the answer to "how did the Soviet government stop the wars?" is "by imposing a uniform national identity".

Just quick addition to Anixx answer

• There was a conflict in 1990 between Uzbeks and the Kyrgyz population in Osh Kirghiz SSR

Because of the examples of what happened to anyone who tried

It's easy to forget just how repressive the Soviet regime was.

In the Baltic states, a guerrilla insurgency operated throughout WWII and into the 1950s. Fighters attempted to kill themselves rather than be captured, because anyone captured by the Soviets would usually be tortured to death.

In 1953, East Germans protested against Soviet rule. The USSR sent the army in. The protests mostly crumbled before serious bloodshed happened, although there were "example" executions of leaders.

In 1956, the Hungarian revolution against Soviet rule was crushed by overwhelming military force. This time the Soviets didn't hold back and thousands died.

In 1968, the Soviet Army invaded Czechoslovakia to stamp out political movements for increased autonomy. Mostly the Czechs did not resist violently, because the lessons from Hungary were clear.

And throughout the span of the USSR, any dissent was generally punished with forced labour in gulags, and a general loss of what rights you did have. This often extended to families as well.

Sorry for bad English. I am Russian and live in Russia. The USSR consisted of 1/7 of the Earth and included a huge number of peoples of both Europe and Asia. Despite this, there were no serious conflicts during the Soviet regime. It's all about total control over society and anti-religious policy. The USSR was an atheistic state, where a struggle was waged against all religions. Also, the words "Russian", "Uzbek", "Armenian", "Ukrainian" and others were replaced with one word - "Soviet". The state pursued a policy of equalizing people not only in the social sphere, where everyone had almost equal rights, regardless of nationality, but in national issues it carried out education of equality between people of different ethnic origins (although some small nations had more rights than large ones). With the collapse of the USSR, all internal politics and ideology collapsed, parts of the USSR ceased to be different from the rest of the World. The socialist glue, with the support of the Russian nation, ceased to hold back historical conflicts. And some conflicts between nations have more than 800 years of history.

Answering Allure's sub-question:

Any idea why these wars and insurgencies were less common during Soviet times as opposed to post-Soviet times? It seems there was nothing from the 1950s to late 1990s too

The period of 1950-1990 was the "cold war", and was characterised by a high level of militarisation. The security and integrity of the state and Party - and the satellite states such as Hungary - was the top priority.

In order to have a civil war two things are required: something to fight with (weapons), and something to fight for (organisation and ideology). Both of these were subject to incredibly heavy levels of control.

Military discipline was strong, so there was little leakage of weapons into private hands. In the post-Soviet period, many weapons were simply sold on the black market by the officers that were supposedly responsible for them. Also, since the USSR was extremely concerned about Western infiltration, and escaping dissidents, the borders were very tightly controlled making it difficult to infiltrate weapons. "The Iron Curtain" described the seemingly-impenetrable border between the West and the Soviet satellite states of Eastern Europe.

Ideological and informational control was also very strong. The opportunities for samizdat publication of political material were limited. Anyone attempting to organize a faction that might fight would be likely to be caught and severely punished.

Finally, to fight you must have an enemy, and two enemies readily existed: for those that believed the propaganda, they could unite against the West. For those that didn't, the biggest and most immediate omnipresent enemy was the state of the USSR itself. In both cases fighting one's immediate neighbors looks like less of a priority.

The risk of individual military units going rogue was mitigated by the usual tactic of empires: conscripts were split up and geographically distributed producing multi-ethnic units that had no particular loyalty to the region they were stationed in.

Yes, there were insurgencies, wars and inter-ethnic conflicts. Not often.

First of all, the Yakut revolt which was part of the Russian civil war, lasted till June 16, 1923. The USSR was established on December 29, 1922. So, the Russian civil war continued in the USSR.

Second, consider the Basmachi movement, which lasted till 1934 but in the 1930s was mostly fought in Afghanistan.

The West Ukrainian and Baltic armed insurgencies lasted till the 1950s.

There was an Armenia-Azerbaijan conflict started in 1988 with deportations and pogroms, with first artillery involvement in 1990.