$C^0$ Transversality and Shadowing Properties

Let $f$ be an Axiom A diffeomorphism of a closed smooth two-dimensional manifold. It is shown that the following statements are equivalent: (a) $f$ satisfies the $C^0$ transversality condition, (b) $f$ has the shadowing property, and (c) $f$ has the inverse shadowing property with respect to a class of continuous methods.