2-symmetric crystallizations and 2-fold branched coverings of S3

For each integer g>1, a class $M_g$ of “2-symmetric” crystallizations, depending on a 2(g+1)-tuple of positive integers satisfying simple conditions is introduced; the “2-symmetry” implies that the represented closed, orientable 3-manifolds are 2-fold covering spaces of $S^3$ branched over a link. Since every closed, orientable 3-manifold M of Heegaard genus $g \le 2$ admits a crystallization belonging to $M_g$, we obtain an easy proof og the fact that M is a 2-fold covering spaces of $S^3$ branched over a link. Further, the class contains all Lins-Mandel crystallizations S(b,l,t,c), with l odd, which are thus proved to represent 2-fold branched coverings of $S^3$.