Quasidiagonal Morphisms and Homotopy

Adapting certain methods of Voiculescu we show that the quasidiagonality of C*-algebras is invariant under completely positive deformations coming from asymptotic morphisms. We define a notion of quasidiagonal morphism. The quasidiagonality of morphisms from exact separable C*-algebras is shown to be invariant under completely positive deformations.