When the ranges of closely-related lineages are large, and overlapping, we can often study introgression at many "replicated" contacts, with different locations and spatial scales. Here we analysed multiple contact zones of the M. edulis complex of marine mussel species, which represent a mosaic distribution of heterogeneously differentiated, semi-isolated genomes. Our aim was to contrast ongoing introgression at the heart of hybrid zones, with past introgression between similar parental populations, at increasing distance from the contact. Using a panel of ancestry-informative SNPs derived from a previous genomic study, we first confirm, with a broader sampling, that local introgression, affecting one but not all of the populations compared, is both widespread and heterogeneous across the genome. Some outlier loci show patterns of complete introgression in certain populations, and an absence of introgression in others. Genomic cline analyses reveal a globally high concordance among loci at a local scale, albeit with signals of asymmetric introgression at a few loci. Enhanced local introgression at specific loci is consistent with the early transfer of adaptive variants after contact, possibly including asymmetric bi-stable variants, or less loaded alleles. Given the mosaic structure of the M. edulis complex, with a succession of genetic barriers to gene flow, variants with enhanced introgression through one barrier can be trapped, maybe transiently, at the next barrier, confining introgression locally. This makes the Mytilus complex an ideal model of the heterogeneous porosity of species barriers.