  We extend Deligne's weight filtration to the integer cohomology of complex
analytic spaces (endowed with an equivalence class of compactifications). In
general, the weight filtration that we obtain is not part of a mixed Hodge
structure. Our purely geometric proof is based on cubical descent for
resolution of singularities and Poincar\'e-Verdier duality. Using similar
techniques, we introduce the singularity filtration on the cohomology of
compactificable analytic spaces. This is a new and natural analytic invariant
which does not depend on the equivalence class of compactifications and is
related to the weight filtration.
