Well, there's a distinction between B-theories of time and eternalism. A B-theory of time is any theory that doesn't privilege the reality of one point in time—usually the present—over another. Eternalism is any theory of time that says the past, present, and future all exist. (The Moving Spotlight Theory is an example of A-theoretic eternalism.)
884heid wrote:
Is the current B theory of time closer to Parmenides or Minkowski's block universe?
There isn't really one B-theory of time. For instance, Minkowski squashes space and time into spacetime in his theory, whereas other B-theoretic eternalists are absolutists about space and relationalists about time[1]. So, B-theoretic eternalists don't need to follow Minkowski in positing “spacetime”.
B-theoretic eternalists don't need to agree with Parmenides either. Unless they deny irreducible dispositions or causal relations, they don't need to deny the act/potency distinction. So, B-theorists can differ from both Minkowski and Parmenides, and the answer to your question depends on the B-theorist.
Alexander Pruss has a couple of good blog posts on B-theoretic analyses of change here and here.
[1]In which case, space and time aren't even in the same ontological category; space is a particular and time, universals. (Not that it's a big deal even if space and time are in the same category. Saying space and time are both relations no more spatializes time than saying horses and sharks are both animals equinizes sharks.)
