On the stable reduction of the Lubin-Tate curve of level two in the equal characteristic case

In the odd residual characteristic case, Weinstein classifies irreducible components in the stable reduction of the Lubin-Tate curve into four types up to purely inseparable map. On the basis of the type theory and the theory of perfectoid space, he shows this. In this paper, in the equal characteristic case, we actually construct the stable covering of the Lubin-Tate curve of level two including the characteristic two case. Our method is purely local, explicit and elementary only on the basis of ideas of Coleman-McMurdy.