Geodesic
Complete topological invariants of Morse--Smale flows and handle decompositions of 3-manifolds
Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 4, pp. 185-196

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We construct a topological invariant for the canonical decomposition on prime and round handles associated with a Morse–Smale flow on a closed 3-manifold. We prove that the flows are topologically equivalent if and only if their invariants coincide. 
@article{FPM_2005_11_4_a13,
     author = {A. O. Prishlyak},
     title = {Complete topological invariants of {Morse--Smale} flows and handle decompositions of 3-manifolds},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {185--196},
     publisher = {mathdoc},
     volume = {11},
     number = {4},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2005_11_4_a13/}
}
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A. O. Prishlyak. Complete topological invariants of Morse--Smale flows and handle decompositions of 3-manifolds. Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 4, pp. 185-196. http://geodesic.mathdoc.fr/item/FPM_2005_11_4_a13/