Perturbations of intermediate C-subalgebras for simple C-algebras

We study uniform perturbations of intermediate C $^* $ -subalgebras of inclusions of simple C $^* $ -algebras. If a unital simple C $^* $ -algebra has a simple C $^* $ -subalgebra of finite index, then sufficiently close intermediate C $^* $ -subalgebras are unitarily equivalent. These intermediate C $^* $ -subalgebras need not be nuclear. The unitary can be chosen in the relative commutant algebra. An immediate corollary is the following: If the relative commutant is trivial, then the set of intermediate C $^* $ -subalgebras is a finite set.