We suggest a way to construct special spines of 2-fold coverings of S 3 branched over links. Let L be a link.
L is trivial.
Given non-trivial L, we construct the following graph. For each double point of a planar projection F of L we draw a circle around it. The intersection points of circles and the link are vertices . If a vertex is not contained in an overpass, we say that it is symmetric with itself. We erase interiors of circles.