Non-removability of Sierpinski carpets

We prove that all Sierpi\'nski carpets in the plane are non-removable for (quasi)conformal maps. More precisely, we show any two $S,S'\subset \hat{\mathbb{C}}$ there exists a homeomorphism $f\colon \hat{\mathbb{C}}\to is conformal $\hat{\mathbb{C}}\setminus S$ and it maps $S$ onto $S'$. The proof topological utilizes ideas of characterization Whyburn. As corollary, obtain partial answer to question Bishop, whether planar continuum with empty interior positive measure can be mapped set zero an exceptional plane, off set.