  In this paper we will promote the 3D index of an ideal triangulation T of an
oriented cusped 3-manifold M (a collection of q-series with integer
coefficients, introduced by Dimofte-Gaiotto-Gukov) to a topological invariant
of oriented cusped hyperbolic 3-manifolds. To achieve our goal we show that (a)
T admits an index structure if and only if T is 1-efficient and (b) if M is
hyperbolic, it has a canonical set of 1-efficient ideal triangulations related
by 2-3 and 0-2 moves which preserve the 3D index. We illustrate our results
with several examples.
