Given a sample of an abstract manifold immerged in some Euclidean space, we describe a way to recover the singular homology of the original manifold. It consists in estimating its tangent bundle-seen as subset of another Euclidean space-in a measure theoretic point of view, and in applying measure-based filtrations for persistent homology. The construction we propose is consistent and stable, and does not involve the knowledge of the dimension of the manifold.