It's an (somewhat distorted) oversimplification to call this a Cold-War style chess game. Both groups are authentic, i.e. people in Western Ukraine genuinely feel closer to the West while people in Eastern Ukraine genuinely do feel closer to Russia. The US influence is nearly non-existent (if you discount Hollywood movies of course) while Russia exerts very significant influence by placing economic pressure (such as banning imports from "misbehaving" countries that were formerly a part of the USSR), providing PR expertise to Russian-supporting political parties, and so on.