The global graph as the complete topological invariant in the class of diffeomorphisms on $\mathbb{M}^3$.

In the present we prove that the global graph is the complete topological invariant in the class of orientation preserving gradient-like diffeomorphisms $f:\mathbb{M}^{3}\to \mathbb{M}^{3}$ whose wandering set contains only noncompact heteroclinic curves.