  The HAWC Collaboration has reported the detection of an extended $\gamma$-ray
emission around the Geminga and Monogem pulsars of a few degree extension. Very
recently, the LHAASO Collaboration released also the data for an extended
$\gamma$-ray emission around the pulsar PSR J0622+3749. This flux can be
explained with electrons and positrons injected from these sources and their
inverse Compton Scattering on the interstellar radiation fields. So far the
size of such $\gamma-$ray halos has been interpreted as the result of the
diffusion coefficient around the sources being about two orders of magnitude
smaller than the average in the Galaxy. However, this conclusion is driven by
the assumption that particles propagate diffusively right away after the
injection without taking into account the ballistic propagation. The
propagation of cosmic-ray leptons in the proximity of the Geminga, Monogem and
PSR J0622+3749 pulsars is examined here considering the transition from the
quasi-ballistic, valid for the most recently injected particles, to the
diffusive transport regime. For typical interstellar values of the diffusion
coefficient, the quasi-ballistic regime dominates the lepton distribution up to
distances of a few tens of parsec from the pulsar for particle energies above
$\sim 10$ TeV. In this regime the resulting $\gamma-$ray source tends to be
rather compact, despite particles travel a long distance. Indeed, for larger
values of the diffusion coefficient, particles propagate ballistically up to
larger distances with the result of a more point-like $\gamma-$ray source. When
such transition is taken into account, a good fit to the HAWC and LHAASO
$\gamma-$ray data around Geminga, Monogem and PSR J0622+3749 is obtained
without the need to invoke a strong suppression of the diffusion coefficient.

High Energy Astrophysical Phenomena