  We deal with a wide class of kinetic equations, $$ \big[ \partial_t +
v\cdot\nabla_x\big] f = \mathcal{L}_v f. $$ Above, the diffusion term
$\mathcal{L}_v$ is an integro-differential operator, whose nonnegative kernel
is of fractional order $s\in(0,1)$ having merely measurable coefficients.
Amongst other results, we are able to prove that nonnegative weak solutions $f$
do satisfy $$ \sup_{Q^-} f \ \leq \ c\inf_{Q^+} f, $$ where $Q^{\pm}$ are
suitable slanted cylinders. No a-priori boundedness is assumed, as usually in
the literature, since we are also able to prove a general interpolation
inequality in turn giving local boundedness which is valid even for weak
subsolutions with no sign assumptions.
  To our knowledge, this is the very first time that a strong Harnack
inequality is proven for kinetic integro-differential-type equations.
  A new independent result, a Besicovitch-type covering argument for very
general kinetic geometries, is also stated and proved.
