  The Milky Way spiral arms are well established from star counts as well as
from the locus of molecular clouds and other young objects, however, they have
only recently started to be observed from a kinematics point of view. Using the
kinematics of thin disc stars in Gaia EDR3 around the extended solar
neighbourhood, we create x-y projections coloured by the radial, residual
rotational, and vertical Galactocentric velocities ($U,\Delta V,W$). The maps
are rich in substructures and reveal the perturbed state of the Galactic disc.
We find that local differences between rotational velocity and the azimuthally
averaged velocity, $\Delta V$, display at least five large-scale kinematic
spirals; two of them closely follow the locus of the Sagittarius-Carina and
Perseus spiral arms, with pitch angles of 9.12$^{\circ}$ and 7.76$^{\circ}$,
and vertical thickness of $\sim400$ pc and $\sim600$ pc, respectively. Another
kinematic spiral is located behind the Perseus arm and appears as a distortion
in rotation velocities left by this massive arm but with no known counterpart
in gas/stars overdensity. A weaker signal close to the Sun's position is
present in our three velocity maps, and appears to be associated with the Local
arm. Our analysis of the stellar velocities in the Galactic disc shows
kinematic differences between arms and inter-arms, that are in favour of Milky
Way spiral arms that do not corotate with the disc. Moreover, we show that the
kinematic spirals are clumpy and flocculent, revealing the underlying nature of
the Milky Way spiral arms.
