you can find a proof in Turaev's book:

http://books.google.fr/books?id=w7dActmezxQC&lpg=PP1&hl=fr&pg=PA183#v=onepage&q&f=false

you can find a proof in Turaev's book Quantum Invariants of Knots and 3-manifolds p183: The bilinear form vanishes on $\lambda_1 \cap \lambda_3$ so it is equivalent to a form on $((\lambda_1 + \lambda_2) \cap \lambda_3)/(\lambda_1 \cap \lambda_3)\simeq ((\lambda_1 + \lambda_3) \cap \lambda_2)/(\lambda_1 \cap \lambda_2)$

$a_3=a_1+a_2\mapsto a_2=a_3-a_1$

and under this isomorphism, the quadratic forms correspond.