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We prove the homotopy equivalence $F\\sim R\\times{\\widetilde{\\cal M}}$ where $R$ is one of the manifolds ${\\mathbb R}P^3$, $S^1\\times S^1$ and the point in dependence on the sign of $\\chi(M)$, and ${\\widetilde{\\cal M}}$ is the universal moduli space of framed Morse functions, which is a smooth stratified manifold. 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