A local calculus for nullhomotopic filling Dehn spheres

We provide a local calculus for the presentation of closed 3–manifolds via nullhomotopic filling Dehn spheres. We use it to define an invariant of closed 3–manifolds by applying the state-sum machinery, and we show how to potentially get lower bounds for the Matveev complexity of P^2-irreducible closed 3–manifolds. We also describe an efficient and simple algorithm for constructing a nullhomotopic filling Dehn sphere of each closed 3–manifold from any of its one-vertex triangulations.