  The recent discovery by Ibata et al. (2013) of a vast thin disk of satellites
(VTDS) around M31 offers a new challenge for the understanding of the Local
Group properties. This comes in addition to the unexpected proximity of the
Magellanic Clouds (MCs) to the Milky Way (MW), and to another vast polar
structure (VPOS), which is almost perpendicular to our Galaxy disk. We find
that the VTDS plane is coinciding with several stellar, tidally-induced streams
in the outskirts of M31, and, that its velocity distribution is consistent with
that of the Giant Stream (GS). This is suggestive of a common physical
mechanism, likely linked to merger tidal interactions, knowing that a similar
argument may apply to the VPOS at the MW location. Furthermore, the VTDS is
pointing towards the MW, being almost perpendicular to the MW disk, as the VPOS
is.
  We compare these properties to the modelling of M31 as an ancient, gas-rich
major merger, which has been successfully used to predict the M31 substructures
and the GS origin. We find that without fine tuning, the induced tidal tails
are lying in the VTDS plane, providing a single and common origin for many
stellar streams and for the vast stellar structures surrounding both the MW and
M31. The model also reproduces quite accurately positions and velocities of the
VTDS dSphs. Our conjecture leads to a novel interpretation of the Local Group
past history, as a gigantic tidal tail due to the M31 ancient merger is
expected to send material towards the MW, including the MCs. Such a link
between M31 and the MW is expected to be quite exceptional, though it may be in
qualitative agreement with the reported rareness of MW-MCs systems in nearby
galaxies.
