A flow \(\phi = (\phi _t)\) on a manifold \(M\) is projectively Anosov when the quotient \(TM /T \phi\) admits a continuous invariant splitting \(E^u \oplus E^s\) and a constant \(C > 0\) such that \(\| (\hat{T}\phi _t)(v^u)\| /\| (\hat{T}\phi _t)(v^s)\| \geq \exp(Ct)\cdot\| v^u\| /\| v^s\| \) for all nonzero vectors \(v^u\in E^u\) and \(v^s\in E^s\) and all \(t > 0\), where \(\| \cdot\| \) is a norm induced by a continuous Riemannian metric on \(M\), while \(\hat{T}\phi _t\) is a linear map on \(TM / T\phi\) induced by the differential \(T\phi _t\). The flow \(\phi\) is regular when the plane fields \(E^u\) and \(E^s\) are smooth of class C\(^1\). Here, the author proves the following result: if \(\phi\) is regular and projectively Anosov while \(M\) a Seifert fibred 3-manifold over a hyperbolic orbifold, then \(\phi\) is isotopic to a quasi-Fuchsian flow lifted to a finite cover provided that the foliations determined by \(E^u\) and \(E^s\) have no compact leaves.