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At section ‘History’, of the second paragraph of the following Wikipedia link, you can read that the Baku-Ceyhan Pipeline, which was the only exit that the Americans managed to find through the NATO-friendly Azerbaijan for the Caspian Sea oil, in a region controlled by the Russians, was proposed to Georgia and Azerbaijan by the Turkish President Demirel in 1992. The pipeline would follow the route Azerbaijan-Georgia-Turkey (Baku-Tbilisi-Ceyhan).
The Russian revenge towards Georgia, was to provide plenty of support to the separatists in the region of Abkhazia, and thus a war started between Georgia and the inhabitants of Abkhazia in 1992. See the first lines of the following wikipedia link.
The Russian revenge towards Azerbaijan, was to provide plenty of support to the Armenian separatists of the region of Karabach in Azerbaijan. As you can read at the third paragraph of the following wikipedia link, Azerbaijan declared independence from the Soviet Union in 1991, and the Armenians of the Karaback asked for their independence as they had done in the past, and the Nagorno-Karabach War started in 1991 (there had been fights in the past too).
The Americans revenge was to support the Chechen separatists, and the first Russia Chechen war started in 1994. See first lines of the following wikipedia link.
You can therefore see how the big powers feed existing conflicts according to their own interests. In all the above cases the conflicts were already there, they were not created by the Russians and the Americans. The Russians and the Americans just used them for their own purposes.