  Anosov families were introduced by A. Fisher and P. Arnoux motivated by
generalizing the notion of Anosov diffeomorphism defined on a compact
Riemannian manifold. Roughly, an Anosov family is a two-sided sequence of
diffeomorphisms (or non-stationary dynamical system) with similar behavior to
an Anosov diffeomorphisms. We show that the set consisting of Anosov families
is an open subset of the set consisting of two-sided sequences of
diffeomorphisms, which is endowed with the strong topology (or Whitney
topology).
