  We establish the uniform in time stability, w.r.t. the marginals, of the
Iterative Proportional Fitting Procedure, also known as Sinkhorn algorithm,
used to solve entropy-regularised Optimal Transport problems. Our result is
quantitative and stated in terms of the 1-Wasserstein metric. As a corollary we
establish a quantitative stability result for Schr\"odinger bridges.
