Some fighting for influence did take place between the two superpowers. Where?

The Cold War was an ongoing political rivalry between the United States and the Soviet Union and their respective allies that developed after World War II. This hostility between the two superpowers was first given its name by George Orwell in an article published in 1945.

Explanation:

on november 6 and 7, 1917 (or october 24 and 25 on the julian calendar, which is why the event is often referred to as the october revolution), leftist revolutionaries led by bolshevik party leader vladimir lenin launched a nearly bloodless coup d'état against the duma's provisional government.