  Coloured Jones and Alexander polynomials are sequences of quantum invariants
recovering the Jones and Alexander polynomials at the first terms. We show that
they can be seen conceptually in the same manner, using topological tools, as
intersection pairings in covering spaces between explicit homology classes
given by Lagrangian submanifolds. The main result proves that the $N^{th}$
coloured Jones polynomial and $N^{th}$ coloured Alexander polynomial come as
different specialisations of an intersection pairing of the same homology
classes over two variables, with extra framing corrections in each case. The
first corollary explains Bigelow's picture for the Jones polynomial with
noodles and forks from the quantum point of view. Secondly, we conclude that
the $N^{th}$ coloured Alexander polynomial is a graded intersection pairing in
a $ \mathbb Z \oplus \mathbb Z_N$-covering of the configuration space in the
punctured disc.
