Specification Diagrams (SD)  are a graphical notation for specifying the message passing behavior of open distributed object systems. SDs facilitate specification of system behaviors at various levels of abstraction, ranging from high-level specifications to concrete diagrams with low-level implementation details. We investigate the theory of may testing equivalence  on SDs, which is a notion of process equivalence that is useful for relating diagrams at different levels of abstraction. We present a semantic characterization of the may equivalence on SDs which provides a powerful technique to relate abstract specifications and refined implementations. We also describe our prototypical implementation of SDs and of a procedure that exploits the characterization of may testing to establish equivalences between finitary diagrams (without recursion).