In Serre's arithmetic he introduces an equivalence relation on the orthogonal bases of a quadratic module $(V,Q)$ through the use of continguity. Recall that a basis $e_1,\ldots, e_k$ of a quadratic module is called orthogonal if there is a direct sum decomposition $$ k\cdot e_1\oplus \cdots \oplus k\cdot e_k $$ such that $$ Q(e_i,e_j) = a_{ij}\delta_{ij} $$ Then, he calls two bases $$ \begin{align*} \underline{e} = (e_1,\ldots,e_k)&& \underline{e}'=(e_1',\ldots,e_k') \end{align*} $$ contiguous if there is some $e_j=e'_j$. He then goes on to prove in theorem 2 that every pair of orthogonal bases can be identified using a sequence/chain of contiguous bases.
My question is: does this contiguity property have any additional interpretation other than "just a tool" for proving the theorem?