A 3-manifold with marked boundary is a pair (M, X), where M is a compact 3-manifold whose (possibly empty) boundary is made up of tori and Klein bottles, and X is a trivalent graph that is a spine of ∂M . A standard skeleton of a 3-manifold with marked boundary (M, X) is a standard sub-polyhedron P of M such that P ∩∂M coincides with X and with ∂P , and such that P ∪ ∂M is a spine of M \ B (whe...