We introduce equivalence relations among asymptotic homomorphisms that in general are stronger than homotopy, but which we show are equivalent to homotopy when the domain is a suspended $C^*$-algebra. As an application, we show that the E-theory of Connes and Higson can be realized as a special case of Kasparov’s KK-theory.
"Homotopy invariance in E-theory." Homology Homotopy Appl. 8 (2) 29 - 49, 2006.