A surprising amount occurred in science, even nuclear research and physical/chemical discovery. While the Communist bloc countries had their own version of Western academic facilities (for example, the Joint Institute for Nuclear Research in Dubna was built as a rough equivalent to CERN), there was a surprising amount of interaction. For example, members of US privately owned universities did travel to the USSR for academic summits, and technological ideas were shared at conferences and through academic papers. There were also more regulated visits between major institutions: Albert Ghiorso and Glenn Seaborg, who were running experiments on transfermium element discovery at Berkeley, visited their Russian counterparts (Flerov and Oganessian) in the 70s. Oganessian's work on discovering cold fusion, first performed at Dubna, was later used to create elements for the first time in Darmstadt, then in West Germany. This was all happening even though the cold war was raging and politicians were arguing about what the elements should be called.
Papers are probably the biggest metric here, because they were freely available to both 'sides' in terms of academia. The race in science was more about the prestige of being first to publish internationally than keeping things secret, and all the main participants in a field knew of and respected each other.
Source: I visited JINR and interviewed Yuri Oganessian about it.
Edit: to clarify for anyone confused; in this instance 'cold fusion' refers to a technique creating elements, not the idea of generating energy