Incidence relationships for the cell decomposition of the moduli space of real hyperelliptic curves. Part 1

Fixing the genus of real hyperelliptic curves, the number of its real ovals and and marking a point at one of them, we get some moduli space. It can be decomposed into non-overlapping cells, enumerated by certain graphs. The weights of the graph satisfy some strict inequalities and define the coordinates of the cell (as well as local coordinates on the moduli space). What happens at the boundary of a cell when the indicated above inequalities are not strict? We pass to a cell of lower dimension, which correspond to certain "perestroika" of the graph.