  We prove that the classical set of moves for standard spines of 3-manifolds
(i.e. the MP-move and the V-move) does not suffice to relate to each other any
two standard skeleta of a 3-manifold with marked boundary. We also describe a
condition on the 3-manifold with marked boundary that tells whether the
generalised set of moves, made up of the MP-move and the L-move, suffices to
relate to each other any two standard skeleta of the 3-manifold with marked
boundary.
  For the 3-manifolds with marked boundary that do not fulfil this condition,
we give three other moves: the CR-move, the T1-move and the T2-move. The first
one is local and, with the MP-move and the L-move, suffices to relate to each
other any two standard skeleta of a 3-manifold with marked boundary fulfilling
another condition. For the universal case, we prove that the non-local T1-move
and T2-move, with the MP-move and the L-move, suffice to relate to each other
any two standard skeleta of a generic 3-manifold with marked boundary.
  As a corollary, we get that disc-replacements suffice to relate to each other
any two standard skeleta of a 3-manifold with marked boundary.
