  We aim to observationally and statistically constrain the influence of flybys
in the formation and evolution of debris disks. We compiled a sample of 254
debris disks with ages between 2 Myr and 8 Gyr that are either part of an
association or isolated, drawing the binary and planetary companions of the
systems mainly from the literature. Using the Gaia eDR3 astrometric data and
radial velocities of our sample, as well as all the sources in a specific
region of the sky, we reconstructed the relative linear motions in the last 5
Myr and made predictions for the next 2 Myr. Relating the Hill radius of each
debris disk system and the closest distances reached by the two sources, we
defined the flyby events in terms of position and time. We find that in the
period between the last 5 Myrs and the next 2 Myrs, 90% of the analyzed systems
have experienced at least a close flyby, while 7% of them have experienced
flybys at distances greater than 0.5R Hill. In particular, 75% of them have
experienced at least one past close encounter and 36% multiple past close
encounters. From the sub-sample of resolved debris disk (41 out of 94), 80% of
the analyzed systems experience at least an encounter within 0.8 pc. From the
subsample of 10 debris disks with planets, half of these systems do show
misalignments between disk and planet, stirring, or asymmetries. Systems with a
misalignment between the planetary orbit and the disk do indeed experience at
least one flyby event. In particular, when the planet orbits have a difference
with the disk inclination higher than about 20 degree, as in the case of HD
38529, we find that multiple close encounters have taken place in the last 5
Myr, as theoretically predicted. The high incidence of encounters, particularly
close encounters, experienced by the systems in the last 5 Myr suggests the
fundamental impact of flybys on the evolution of debris disks.
