Notions of equivalence which guarantee intersubstitutability w.r.t. further modifications have received considerable interest in nonmonotonic reasoning. This paper is within the context of abstract argumentation and we focus on the most general form of a dynamic scenarios, so-called updates as well as certain sub-classes, namely local, normal and arbitrary deletions. We provide characterization theorems for the corresponding equivalence notions and draw the relations to the recently proposed kinds of expansion equivalence [15, 3]. Many of the results rely on abstract concepts like context-free kernels or semantics satisfying isolate-inclusion. Therefore, the results may apply to future semantics as well as further equivalence notions.