Topological invariance of the intersection homology of a pseudomanifold isone of the main properties of this homology. It has been first established byM. Goresky and R. MacPherson and revisited by H. King some years later, withthe introduction of an intrinsic stratification, $X^*$, associated to apseudomanifold $X$. In this work, we show that some topological invariance remains true in thecase of general perversities, defined on each stratum and not only from thecodimension. For doing that, we introduce in this general framework, theconcept of K-perversities which correspond to GM-perversities. From aK-perversity, $\bar{p}$, on a pseudomanifold $X$, we construct a perversity,$\bar{q}$, on $X^*$ such that $H_{*}^{\overline{p}}(X)\congH_*{\overline{q}}(X^*)$. We study also the extension of this result to avariation of intersection homology, more adapted to large perversities.\\