In this paper we build Non-singular Morse-Smale flows on S^3 with unknotted
and unlinked saddle orbits by identifying fat round handles along their
boundaries. This way of building the flows enables to get their phase
portraits. We also show that the presence of heteroclinic trajectories imposes
an order in the round handle decomposition of these flows; this order is total
for NMS flows composed of one repulsive, one attractive and n unknotted saddle
orbits, for n >1.Comment: 15 page