We consider a counter-rotating torus orbiting a central Kerr black hole (BH) BH ) with dimensionless spin a , and its accretion flow into the BH , in an agglomerate of an outer counter-rotating torus and an inner co-rotating torus. This work focus is the analysis of the inter-disks inversion surfaces. Inversion surfaces are spacetime surfaces, defined by the condition u = 0 on the flow torodial velocity, located out of the BH ergoregion, and totally embedding the BH . They emerge as a necessary condition, related to the spacetime frame-dragging, for the counter-rotating flows into the central Kerr BH . In our analysis we study the inversion surfaces of the Kerr spacetimes for the counter-rotating flow from the outer torus, impacting on the inner co-rotating disk. Being totally or partially embedded in (internal to) the inversion surfaces, the inner co-rotating torus (or jet) could be totally or in part "shielded", respectively, from the impact with flow with au < 0. We prove that, in general, in the spacetimes with a < 0.551 . 551 the co-rotating toroids are always external to the accretion flows inversion surfaces. For 0.551 . 551 < a < 0.886, . 886, co-rotating toroids could be partially internal (with the disk inner region, including the inner edge) in the flow inversion surface. For BHs with a > 0.886, . 886, a co-rotating torus could be entirely embedded in the inversion surface and, for larger spins, it is internal to the inversion surfaces. Tori orbiting in the BH outer ergoregion are a particular case. Further constraints on the BHs spins are discussed in the article.