  We present the results of a set of numerical simulations aimed at studying
reionization at galactic scale. We use a high resolution simulation of the
formation of the Milky Way-M31 system to simulate the reionization of the local
group. The reionization calculation was performed with the post-processing
radiative transfer code ATON and the underlying cosmological simulation was
performed as part of the CLUES project. We vary the source models to bracket
the range of source properties used in the literature. We investigate the
structure and propagation of the galatic ionization fronts by a visual
examination of our reionization maps. Within the progenitors we find that
reionization is patchy, and proceeds locally inside out. The process becomes
patchier with decreasing source photon output. It is generally dominated by one
major HII region and 1-4 additional isolated smaller bubbles, which eventually
overlap. Higher emissivity results in faster and earlier local reionization. In
all models, the reionization of the Milky Way and M31 are similar in duration,
i.e. between 203 Myr and 22 Myr depending on the source model, placing their
zreion between 8.4 and 13.7. In all models except the most extreme, the MW and
M31 progenitors reionize internally, ignoring each other, despite being
relatively close to each other even during the epoch of reionization. Only in
the case of strong supernova feedback suppressing star formation in haloes less
massive than 10^9 M_sun, and using our highest emissivity, we find that the MW
is reionized by M31.
