Topological classification of gradient-like diffeomorphisms with finite number of heteroclynic curves on $\mathbf{M}^3$

In this paper we get necessary and sufficient conditions of topological conjugacy in the class of orientation preserving gradient-like diffeomorphisms $f:\mathbf{M}^{3}\rightarrow\mathbf{M}^{3}$ satisfies the condition: the wandering set of each diffeomorphism contains only noncompact heteroclinic curves.