Particles that end up in the MW sub-halo (in red) and in the M31 (in blue) by the present day, traced back to various redshifts for one of our realisations. Each column shows a different redshift. The coordinate system has been rotated and scaled such that the MW and M31 main progenitors are at (0,0,0) and (1,0,0), respectively, at all times (indicated with white dots). Top row: Approximately edge-on view of the Local Sheet. Bottom row: Face-on view.