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We provide explicit formulaes for the first Kantorovich-Wasserstein distancebetween stationary measures for iterated function scheme on the unit interval.In particular, we consider two stationary measures with differentconfigurations of the weights associated to the same iterated function schemeswith disjoint images composed of: $k$ positive contractions or $2$ contractionsof different sign. We also study the case of two stationary measures associatedto different iterated function schemes.

The Wasserstein distance between stationary measures associated to iterated function schemes on the unit interval