Left: Gaia extended kinematic maps (Fig. 8 of Paper I) with the over-plotting of the representation of the spiral arms: four main spiral arms follow the model of Vallée (2017) and the local spur modeled by Hou & Han (2014): upper panel, radial velocity; bottom panel, vertical velocity. Right: Gaia extended kinematic maps introducing a correction to the zero-point bias of parallaxes π_c = π + 0.03 mas (Fig. 16 of Paper I).