Should I update my arXiv submission after it's been reviewed and published OA in a Springer journal?
Under Springer Open Choice, you retain copyright and the journal releases the published article under a CC-BY license.

So:


By the terms of CC-BY, everyone can make a copy the published paper and redistribute it under the same license, including on Arxiv.
Even better: you, the copyright holder, can relicense the paper to anyone, with the terms you want. As long as you don't give them an "exclusive right to distribute", of course, because you cannot take back the rights you have already granted others.


Some Open Choice journals use CC-BY-NC, though which may make redistribution under the first method trickier, because Arxiv does not have an option for CC-BY-NC. The other method is always ok, though.

Note: I am not a lawyer.