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We introduce moduli spaces of stable perverse coherent systems on small crepant resolutions of Calabi–Yau 3-folds and consider their Donaldson–Thomas-type counting invariants. The stability depends on the choice of a component ( = a chamber) in the complement of finitely many lines ( = walls) in the plane. We determine all walls and compute generating functions of invariants for all choices of chambers when the Calabi–Yau is the resolved conifold. For suitable choices of chambers, our invariants are specialized to Donaldson–Thomas, Pandharipande–Thomas and Szendroi invariants.

Counting Invariant of Perverse Coherent Sheaves and its Wall-crossing