  How the cosmic web feeds halos, and fuels galaxy formation is an open
question with wide implications. This study explores the mass assembly in the
Local Group within the context of the local cosmography by employing
simulations whose initial conditions have been constrained to reproduce the
local environment. The goal of this study is to inspect whether the direction
of accretion of satellites on to the Milky Way and Andromeda galaxies, is
related to the cosmic web. The analysis considers the three high-resolution
simulations available in the HESTIA simulation suite, as well as the derived
velocity shear and tidal tensors. We notice two eras in the Local Group
accretion history, delimited by an epoch around $z \approx 0.7$. We also find
that satellites can travel up to $\sim 4$ Mpc, relative to their parent halo
before crossing its viral radius $R_{200}$. Finally, we observe a strong
alignment of the infall direction with the axis of slowest collapse $\vec{e_3}$
of both tidal and shear tensors, implying satellites of the Local Group
originated from one particular region of the cosmic web and were channeled
towards us via the process of accretion.This alignment is dominated by the
satellites that enter during the early infall era, i.e $z>0.7$.
