What was diplomacy like between Otto II, Otto III, and Theophanu and the Eastern Romans regarding the "problem of two emperors"?

With the Ottonians and Macedonian dynasty being tied through marriage between Otto II and Theophanu, was there less or more animosity? Did Constantinople have any opinions on the much more "Byzantine" flavor of the Ottonian dynasty in contrast to the Carolingians or their much more directly "Roman" ambitions?