Classification of Surface A-Diffeomorphisms with no Zero-Dimensional Basic Sets

On a closed orientable surface, we consider the set of axiom A diffeomorphisms whose nonwandering sets consist of connected one-dimensional expanding attractors and contracting repellers (any attractor/repeller is locally homeomorphic to the product of segment and Cantor set). This set consists of $\Omega$-stable diffeomorphisms and structurally unstable diffeomorphisms. We classify such diffeomorphisms up to the global conjugacy on its nonwandering sets.