  We study transport across junctions of a Weyl and a multi-Weyl semimetal (WSM
and a MSM) separated by a region of thickness $d$ which has a barrier potential
$U_0$. We show that in the thin barrier limit ($U_0 \to \infty$ and $d \to 0$
with $\chi=U_0 d/(\hbar v_F)$ kept finite, where $v_F$ is velocity of
low-energy electrons and $\hbar$ is Planck's constant), the tunneling
conductance $G$ across such a junction becomes independent of $\chi$. We
demonstrate that such a barrier independence is a consequence of the change in
the topological winding number of the Weyl nodes across the junction and point
out that it has no analogue in tunneling conductance of either junctions of
two-dimensional topological materials (such as graphene or topological
insulators) or those made out of WSMs or MSMs with same topological winding
numbers. We study this phenomenon both for normal-barrier-normal (NBN) and
normal-barrier-superconductor (NBS) junctions involving WSMs and MSMs with
arbitrary winding numbers and discuss experiments which can test our theory.
