Let (M,��,��,��,g) be a compact quasi-regular Sasakian 5-manifold with finite cyclic quotient foliation singularities of type (1/r)(1,a). First, we derive the foliation minimal model program by applying the resolution of cyclic quotient foliation singularities. Secondly, based on the study of local model of resolution of foliation singularities, we prove the foliation canonical surgical contraction or the foliation extremal ray contraction under the Sasaki-Ricci flow. As a consequence, we prove a Sasaki analogue of analytic minimal model program with the Keahler-Ricci flow due to Song-Tian and Song-Weinkove.

arXiv admin note: text overlap with arXiv:1003.0718, arXiv:1004.2461, arXiv:1212.3653 by other authors. substantial text overlap with arXiv:2203.00374