Dotted links, Heegaard diagrams and coloured graphs for PL 4-manifolds

The present paper is devoted to establish a connection between the 4-manifold representation method by dotted framed links (or - in the closed case - by Heegaard diagrams) and the so called crystallization theory, which visualizes general PL-manifolds by means of edge-coloured graphs.In particular, it is possible to obtain a crystallization of aclosed 4-manifold $M^4$ starting from a Heegaard diagram$(\#_m(S^1 X S^2), \omega),$ and the algorithmicity of the whole process depends on the effective possibility of recognizing $(\#_m(S^1 X S^2), \omega)$ to be a Heegaard diagram by crystallization theory