  We study metric spheres Z obtained by gluing two hemispheres of the Euclidean
sphere along an orientation-preserving homeomorphism mapping the equator onto
itself, where the distance on Z is the canonical distance that is locally
isometric to the spherical distance off the seam. We show that if Z is
quasiconformally equivalent to the sphere, in the geometric sense, then g is a
welding homeomorphism with conformally removable welding curves. We also show
that g is bi-Lipschitz if and only if Z has a 1-quasiconformal parametrization
whose Jacobian is comparable to the Jacobian of a quasiconformal mapping from
the Euclidean sphere onto itself. Furthermore, we show that if the inverse of g
is absolutely continuous and g admits a homeomorphic extension with
exponentially integrable distortion, then Z is quasiconformally equivalent to
the Euclidean sphere.
