Invariant of free knots

Question

In section 5. of https://arxiv.org/pdf/0912.5348.pdf, prof. Manturov gives a definition of an invariant of free knots, the $[\cdot]$ invariant. It is considered as an element of the space $\mathbb{Z}_2B$, where $B$ is the set of all equivalences classes of framed 4-valent graphs with one unicursal component modulo second Reidemeister moves. Shall we consider two isomorphic framed 4-graphs as the same element in $B$? (i.e. does the particular numbering of vertices have the meaning?)