On Peixoto's Conjecture for Flows on Non-orientable 2-Manifolds

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Let M be a non-orientable compact 2-manifold of genus 4. Then there exists a family of quasi-minimal, Kupka-Smale smooth vector fields Xᵣ in M, depending smoothly on 0<=r<e, such that, for some flow box V in M of X₀, and for all 0<=r,v<e, (1) Xᵣ restricted to V is a flow box; (2) If r is not equal to v, Xᵣ is a C∞--twist perturbation of Xᵥ localized in V; (3) Xᵣ and Xᵥ are topologically equivalent.