Summary of the underdensity thresholds and corresponding relationships introduced in this work. In the first row we report the values relative to the shell-crossing phenomenon (subscript sc) together with their corresponding numerical values, shown in the white tags. In the second row we list the density contrasts values used in our analysis. The quantities circled in red refer to density contrasts defined in nonlinear theory (superscript NL), while those circled in yellow are defined in linear theory (superscript L). The latter are used to compute the Vdn model and are obtained from the former by means of Eq. (8). All the quantities listed in the central and in the right columns are defined in the density field traced by unbiased objects, i.e. DM particles (subscript DM). On the far left we report instead the underdensity threshold used to define void in this paper. It has a value of −0.7 and is computed in the density field traced by galaxies (subscript tr). To find its corresponding value in the underlying DM field we make use of Eq. (7).