Branched covers of twist-roll spun knots

We prove that the double branched cover of a twist-roll spun knot in S⁴ is smoothly preserved when four twists are added, and that the double branched cover of a twist-roll spun knot connected sum with a trivial projective plane is preserved after two twists are added. As a consequence, we conclude that a family of homotopy CP²s recently constructed by Miyazawa are each diffeomorphic to CP².