  In this work, we aim at investigating the morphology evolution of Milky Way
mass-like dark matter haloes selected from the CIELO and IllustrisTNG Projects.
The connection between halo shapes and their environment has been studied in
previous works at z=0 but their connection remains yet to be fully understood.
We focus on the evolution across cosmic time of the halo shapes and the
relation with the infalling material, using hydrodynamical simulations. Our
findings show that haloes tend to be more triaxial at earlier times as a
consequence of stronger accretion in the direction of the filaments. As the
haloes evolve towards a dominant isotropic accretion mode and relaxation, their
shape at 20 percent of the virial mass becomes more spherical. In agreement
with previous results, baryons have an important effect within the inner
regions of the haloes, driving them from triaxial to rounder shapes. We also
find a correlation between the strength of the quadrupole infalling mode and
the degree of ellipticity of the haloes: as the filament strength decreases
steadily with redshift, the haloes became more spherical and less elliptical.
