The upper one is exactly right. Thanks for providing a figure as it helps to discuss things. And see the answer I just posted to your other question.
You can see that the upper figure has to be right because the MPS in principle extends much further beyond the sites you show above, but because of the left and right orthogonality property, the tensors outside of the support of "O" cancel leaving identity matrices on the left and right. These become the lines connecting the top (bra) to the bottom (ket).
The lower one wouldn't be correct for a number of reasons. One reason is what I just wrote above about first writing out the full MPS then canceling most of the tensors (it helps to imagine it not as a truly infinite MPS but as a very large finite MPS with open boundaries some unspecified distance away). Another reason it wouldn't be correct is because it would seem to make the states look as if they are periodic states on a system of size N, whereas they are actually wavefunctions on a much larger, or even infinite, system.