The main relationship between the United States and the Union of Soviet Socialist Republics is that they both avoided open military combat.
The cold war is an unarmed conflict between United States and Union of Soviet Socialist Republics which came to an end in 1991 after the fall of the Soviet Union.
The patterns of relationship that existed between is an indirect fight which resulted in anti-communist suspicions and international incidents.
Therefore, the main relationship between the United States and the Union of Soviet Socialist Republics is that they both avoided open military combat.
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