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We study the stability of covers of simplicial complexes. Given a map f:Y→ X that satisfies almost all of the local conditions of being a cover, is it close to being a genuine cover of X? Complexes X for which this holds are called cover-stable. We show that this is equivalent to X being a cosystolic expander with respect to non-abelian coefficients. This gives a new combinatorial-topological interpretation to cosystolic expansion which is a well studied notion of high dimensional expansion. AsarXiv:1909.08507v1 fatcat:l4csd67gyndhnflnw2rc2miln4