We show that: (1) on any open manifold other than the line or plane, there exist nonsingular flows with Ω ≠ ∅ \Omega \, \ne \,\emptyset which can be perturbed, in the strong C r {C^r} topology (any r), to flows with Ω ≠ ∅ \Omega \, \ne \,\emptyset , and that (2) on certain open 3-manifolds there exist flows with Ω ≠ ∅ \Omega \, \ne \,\emptyset which cannot be approximated, in the strong C 1 {{\mathcal {C}}^1} topology, by flows satisfying both Ω ≠ ∅ \Omega \, \ne \,\emptyset and no C 1 {{\mathcal {C}}^1} Ω \Omega -explosions. These examples give partial negative answers to the conjecture of Takens and White, that the completely unstable flows with the strong C r {{\mathcal {C}}^r} topology equal the closure of their interior.