Remodeling a DS-diagram into one with E-cycle (Q1583808)

The paper is concerned with the combinatorial representation of compact 3-manifolds with boundary by standard spines [\textit{B. G. Casler}, Proc. Am. Math. Soc. 16, 559-566 (1965; Zbl 0129.15801)]. It is well known that two 3-manifolds are homeomorphic if and only if they have a standard spine in common. Subsequently, special classes of spines (called flow-spines) for closed 3-manifolds were constructed by using a flow on the manifold [\textit{I. Ishii}, Tokyo J. Math. 9, 505-525 (1986; Zbl 0697.57004)]. The authors give an algorithm to deform a standard spine to a flow-spine in a given closed 3-manifold. This algorithm is based on the theory of DS-diagrams which describe standard spines by graph-theoretical tools [see for example \textit{H. Ikeda} and \textit{Y. Inoue}, Kobe J. Math. 2, 169-185 (1985; Zbl 0602.57008)].