  We introduce three generalizations of homotopy equivalence in digital images,
to allow us to express whether a finite and an infinite digital image are
similar with respect to homotopy.
  We show that these three generalizations are not equivalent to ordinary
homotopy equivalence, and give several examples. We show that, like homotopy
equivalence, our three generalizations imply isomorphism of fundamental groups,
and are preserved under wedges and Cartesian products.
