Were civilian aircraft allowed to overfly the Soviet Union?
During the Cold War, Soviet airspace was very restricted to other countries. Flights from the US often had to follow polar routes to Asia and Europe that avoided entering Soviet airspace. The end of the Cold War allowed new routes to be used.


Source

Flights to the USSR were allowed on a limited basis, often in conjunction with service by Aeroflot. Air Canada had the first service (via Copenhagen) from North America in 1966. Some flights were allowed to cross the USSR (JAL started in 1985) but would often stop on Moscow. Otherwise, Anchorage was a typical stop on such a route. International relations may have improved since the Soviet era, but even today not every airline gets permission to overfly Russia.

The strict policies are the reason that flights such as Korean Air Lines flight 007 were shot down when deviating from these routes, and the flight of Mathias Rust to Moscow was a big deal.