Оn classification of Morse-Smale diffeomorphisms with trivial embedded separatrices on $3$-manofolds

We define the trivial embedding of separatrixes and prove that Peixoto graph (enriched by automorphism) is complete invariant in class $G_1(M^{3})$ of orientation preserve Morse-Smale diffeomorphisms on closed orientable $3$-manifold $M^3$ such that for any $f\in G_1(M^3)$ the set of unstable separatrixes is trivial and has dimension $1$.