This paper corresponds to Section 8 of arXiv:1912.05774v3 [math.GT]. The
contents until Section 7 are published in Annali di Matematica Pura ed
Applicata as a separate paper. In that paper, it is proved that for any
positive flow-spine P of a closed, oriented 3-manifold M, there exists a unique
contact structure supported by P up to isotopy. In particular, this defines a
map from the set of isotopy classes of positive flow-spines of M to the set of
isotopy classes of contact structures on M. In this paper, we show that this
map is surjective. As a corollary, we show that any flow-spine can be deformed
to a positive flow-spine by applying first and second regular moves
successively.Comment: 17 pages and 22 figures. This paper covers Section 8 of the preprint
arXiv:1912.05774v3 [math.GT]. The part until Section 7 is covered in
arXiv:1912.05774v4 [math.GT] as a separate pape