An algorithm producing a standard spine of a 3-manifold presented by surgery along a link

We provide a simple algorithm which produces a (branched) standard spine of a 3-manifold presented by surgery along a framed link in S^3, giving an explicit upper bound on the complexity of the spine in terms of the complexity of a diagram of the link. As a corollary, we get an easy constructive proof of Casler’s result on the existence of a standard spine for a closed 3-manifold. We also describe an o-graph which represents the spine.