  Here, we study the dichotomy of the escaping atmosphere of the newly
discovered close-in exoplanet AU Mic b. On one hand, the high EUV stellar flux
is expected to cause a strong atmospheric escape in AU Mic b. On the other
hand, the wind of this young star is believed to be very strong, which could
reduce or even inhibit the planet's atmospheric escape. AU Mic is thought to
have a wind mass-loss rate that is up to $1000$ times larger than the solar
wind mass-loss rate ($\dot{M}_\odot$). To investigate this dichotomy, we
perform 3D hydrodynamics simulations of the stellar wind--planetary atmosphere
interactions in the AU Mic system and predict the synthetic Ly-$\alpha$
transits of AU Mic b. We systematically vary the stellar wind mass-loss rate
from a `no wind' scenario to up to a stellar wind with a mass-loss rate of
$1000~\dot{M}_\odot$. We find that, as the stellar wind becomes stronger, the
planetary evaporation rate decreases from $6.5\times 10^{10}$ g/s to half this
value. With a stronger stellar wind, the atmosphere is forced to occupy a
smaller volume, affecting transit signatures. Our predicted Ly-$\alpha$
absorption drops from $\sim 20\%$, in the case of `no wind' to barely any
Ly-$\alpha$ absorption in the extreme stellar wind scenario. Future Ly-$\alpha$
transits could therefore place constraints not only on the evaporation rate of
AU Mic b, but also on the mass-loss rate of its host star.
