As a proxy for cosmic evolution, I will compute the rate of merging critical points as a function of smoothing scale from the initial cosmic landscape to forecast special events driving the assembly of dark halos. Beyond the peak-saddle mergers, I will consider all sets of critical points coalescence, including wall-saddle to filament-saddle and wall-saddle to minima, as they impact the topology of galactic infall, and in particular filament disconnection. The rate of filament coalescence will be compared to the merger rate of halos while computing the two-point clustering of these critical events. This correlation is qualitatively consistent the preservation of the connectivity of dark halos, and the impact of the large scale structures on assembly bias. I will estimate the relationship between merger rates ratio and critical counts ratio. I will discuss applications to cosmology, astrophysics and other fields of research, such as the dependence of void mergers on cosmic parameters and primordial non gaussianity.