Distribution of the Lyα nebula velocity shift with respect to the quasar Lyα emission peak. The plot shows histograms of the velocity shifts (v_m1) computed from the first moment of the flux distribution (Tables A.2 and C.1) for the extended Lyα emission around the bright (green) and faint (orange) QSO MUSEUM samples. The size of each histogram bin corresponds to 163 km s⁻¹. We also show the median v_m1 for bins A2 and A3 (Figure 12) at the respective number of systems. Their error bars indicate the full range of velocity shifts within A2 and A3.