Perturbations of crossed product C-algebras by amenable groups

We study uniform perturbations of crossed product C\(^*\)-algebras by amenable groups. Given a unital inclusion of C\(^*\)-algebras \(C\subseteq D\) and sufficiently close separable intermediate C\(^*\)-subalgebras \(A\), \(B\) for this inclusion with a conditional expectation from \(D\) onto \(B\), if \(A=C\rtimes G\) with \(G\) discrete amenable, then \(A\) and \(B\) are isomorphic. Furthermore, if \(C\subseteq D\) is irreducible, then \(A=B\).