The spherically symmetric dust dominated models, ususlly called Lemaître-Tolman-Bondi models, are investigated. The final/initial behavior of such a Universe is studied in proximity of collapse/generation times by an expansion in fractional Puiseux series. Our analysis shows that in a short range of collapse/generation interval the spatial initial curvature doesn’t influence the evolution: in proximity of these times, a generic Lemaître-Tolman-Bondi Universe evolves analogously to the initially spatially Euclidean model.