How common were direct flights between the United States and the Soviet Union?

You might be interested in some previous threads on travel between the United States and the Soviet Union:

Cold war travel from the West to the Soviet Union, possible? - 2 comments, over 6 months old.
Very brief, but both comments give overviews of travel (and a travel agency!) between the USA and the USSR.
How isolated was the Soviet Union? - 6 comments, over 2 years old.
The commenters her go into travel between the West and Soviet satellite states.
Did Soviet scientists attend international science conferences? - 6 comments, over 2 months old.
One commenters gives a strong overview of how often and under what restrictions Soviet scientists were allowed to go to foreign countries and how that changed over the course of the Cold War.