  We give a possible generalization of Lutz twist to all dimensions. This
reproves the fact that every contact manifold can be given a non-fillable
contact structure and also shows great flexibility in the manifolds that can be
realized as cores of overtwisted families. We moreover show that $R^{2n+1}$ has
at least three distinct contact structures.
  This version of the paper contains both the texts of the published version of
the paper together with an Erratum to the published version appended to the
end.
