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In this paper we build Non-singular Morse-Smale flows on S^3 with unknottedand unlinked saddle orbits by identifying fat round handles along theirboundaries. This way of building the flows enables to get their phaseportraits. We also show that the presence of heteroclinic trajectories imposesan order in the round handle decomposition of these flows; this order is totalfor NMS flows composed of one repulsive, one attractive and n unknotted saddleorbits, for n >1.

Fat handles and phase portraits of Non Singular Morse-Smale flows on S^3 with unknotted saddle orbits