Tensions between Russia and NATO have continued to intensify as the conflict in Ukraine grinds on. Both NATO and Russia have exchanged barbs, criticizing the other side for its role in a conflict that has already killed more than 4,300 people. NATO has repeatedly said that Russia has been providing direct and indirect military aid to the separatists in eastern Ukraine. Russia has accused NATO of overthrowing the previous Ukrainian government, backing fascists in Ukraine, and expanding the organization in alleged violation of earlier agreements. In response to Russia's frequent claims, NATO has released a fact sheet that is also available in Russian and Ukrainian. This isn't the first time that the world's most powerful military alliance or its members have directly engaged with Moscow online. NATO released a similar fact-sheet in April. And Canada's NATO delegation caustically trolled the Kremlin after the country's invasion of eastern Ukraine in August, with a map reminding Russia of where its borders ended. We have highlighted the most interesting facts that NATO has sought to clarify below. Russian Claim: NATO promised it would not expand east into the Baltics and eastern Europe following German reunification. NATO Rebuttal: Though often repeated as fact, the NATO fact sheet notes that there's no real evidence that such a quid pro quo was ever reached. Indeed, it couldn't have been reached — when Germany was re-unified in 1990, many of the countries targeted for NATO expansion later on were still under Soviet domination or were members of the rival Warsaw Pact. Per NATO, even Mikhail Gorbachev, then the Soviet premier, says that the "neither NATO nor Soviet leaders ever brought up the issue of NATO expansion." Russian Claim: NATO enlargement has destabilized the Balkans NATO Rebuttal: This is another frequent Russian claim, often tied to the idea that NATO waged aggressive war against Serbia during the Balkan wars of the 1990s (see next item). In fact, the NATO fact-check claims, the alliance's Balkan members (Albania, Croatia, Slovenia, and Greece) have enjoyed enhanced security and democratic development thanks to their membership in the organization. Russian Claim: Russian action in Crimea was identical to NATO action in Crimea NATO Rebuttal: The accusation that the NATO states waged an aggressive invasion of Serbia during the Kosovo crisis of 1999 is a common Russian talking point used to justify Moscow's annexation of Crimea. In fact, NATO notes, allied military action in Kosovo was the result of nearly a decade of failed attempts at peaceably solving a longstanding and violent dispute between Serbia's oppressive and human rights-abusing government and Kosovo's ethnic Albanian majority. Crimea, on the other hand, was never in dispute and never the focal point of a long-running crisis — until Russia annexed the peninsula in March, that is. Russian Claim: The Ukrainian government is illegitimate and is dominated by Nazis and fascists NATO Rebuttal: "Ukraine's president was elected with a clear majority in May 25 in an election that the Organization for Security and Co-Operation in Europe (OSCE) characterized as free and fair," the fact-check notes. As for those Nazis and fascists that Moscow seems so worried about, "far right parties received less than 5%, the legal limit for parties to become represented in parliament."SEE ALSO: Here are 2 ways Russia's provocative stunts could lead to war Join the conversation about this story »