  Petrov and Pilyugin (2015) generalized a notion of $C^0$ transversality of
Sakai (1995) using smooth curves. Their definition involves only continuous
maps from ${\mathbb R}^n$ to a manifold, which is a purely topological one.
They also provided a sufficient condition for the $C^0$ transversality in terms
of homological nature. In this paper, we prove that such a homological
condition of Axiom A diffeomorphisms is sufficient for enjoying the shadowing
property. Moreover, it is proved that the $C^0$ transversality of Axiom A
diffeomorphisms with codimension one basic sets implies the homological
condition.
