The authors present a combinatorial representaion of gluing 3-manifolds and their special spines. This is done using graphs encoded by \(\gamma\)-tuples of non-negative integers. More precisely, they use the result of Casler which states that two 3-manifolds with homeomorphic special spines are homeomorphic. Then, since homeomorphic spines are related by two types of moves, they can study the topology of these 3-manifolds with computers. Moreover they give a procedure to determine the hyperbolicity equations of a gluing manifold.