  During the EoR, the first stars and galaxies appear while creating ionized
bubbles that will eventually percolate near z=6. These ionized bubbles and
percolation process are nowadays under a lot of scrutiny since observations of
the HI gas will be carried on in the next decade with e.g. the SKA
radiotelescope. Studies of the EoR are performed on semi-analytical and fully
numerical cosmological simulations to investigate e.g. the topology of the
process. We analyse the topology of EoR models through regions that are under
the radiative influence of ionization sources. They are associated with peak
patches of reionization redshift (zreion) field, for which we measure their
general properties (e.g. number, size, shape, orientation). We aim at gaining
insights on the geometry of the reionization process and how it relates to the
matter distribution for example. We also assess how such measurements can be
used to quantify the influence of physical parameters on the reionization
models or the differences between fully numerical simulations and
semi-analytical models. We use the DisPerSE framework (which applies the Morse
theory and the persistent homology) on different EoR scenarios through gas
density and zreion maps. We find that we can distinguish between EoR models
with different sources using simple analyses on the number, shape and size
distributions of the peak patches. For every model, we statistically show that
they are rather prolate and aligned with the gas filaments. We briefly
highlight that the percolation process can be followed studying zreion fields
with different persistence thresholds. We show that fully numerical EMMA
simulations can be made consistent with 21cmFAST models in this topological
framework as long as the source distribution is diffuse enough.
