Good potentials for almost isomorphism of countable state Markov shifts
  Almost isomorphism is an equivalence relation on countable state Markov shifts which provides a strong version of Borel conjugacy; still, for mixing SPR shifts, entropy is a complete invariant of almost isomorphism. In this paper, we establish a class of potentials on countable state Markov shifts whose thermodynamic formalism is respected by almost isomorphism. 
Jerome Buzzi (CMLS), Mike M. Boyle, Ricardo Gomez