  Ott, Tomforde, and Willis proposed a useful compactification for one-sided
shifts over infinite alphabets. Building from their idea we develop a notion of
two-sided shift spaces over infinite alphabets, with an eye towards
generalizing a result of Kitchens. As with the one-sided shifts over infinite
alphabets our shift spaces are compact Hausdorff spaces but, in contrast to the
one-sided setting, our shift map is continuous everywhere. We show that many of
the classical results from symbolic dynamics are still true for our two-sided
shift spaces. In particular, while for one-sided shifts the problem about
whether or not any $M$-step shift is conjugate to an edge shift space is open,
for two-sided shifts we can give a positive answer for this question.
