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We describe all possible topological structures of Morse-Smale flows withoutclosed trajectories on a three-dimensional sphere, which have two sources, twosinks, one saddle of Morse index 1, one saddle of Morse index 2, and no morethan 10 saddle connections. To classify such flows, a generalized Heegaarddiagram or Pr-diagram is used, which in this case consists of a sphere and twoclosed curves, the intersection points of which correspond to saddleconnections. We have found all possible, up to homeomorphism, ways to embed twocircles in a 2-sphere with no more than 10 points of transversal intersectionand construct its planar visualisations.

Visualization of Morse flow with two saddles on 3-sphere diagrams