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(Abridged) Context. Core condensation is a critical step in the star-formation process, but is still poorly characterized observationally. Aims. We have studied the 10 pc-long L1495/B213 complex in Taurus to investigate how dense cores have condensed out of the lower-density cloud material. Results. From the N$_2$H$^+$ emission, we identify 19 dense cores, some starless and some protostellar. They are not distributed uniformly, but tend to cluster with relative separations on the order of 0.25 pc. From the C$^{18}$O emission, we identify multiple velocity components in the gas. We have characterized them by fitting gaussians to the spectra, and by studying the distribution of the fits in position-position-velocity space. In this space, the C$^{18}$O components appear as velocity-coherent structures, and we have identified them automatically using a dedicated algorithm (FIVe: Friends In Velocity). Using this algorithm, we have identified 35 filamentary components with typical lengths of 0.5 pc, sonic internal velocity dispersions, and mass-per-unit-length close to the stability threshold of isothermal cylinders at 10 K. Core formation seems to have occurred inside the filamentary components via fragmentation, with a small number of fertile components with larger mass-per-unit-length being responsible for most cores in the cloud. At large scales, the filamentary components appear grouped into families, which we refer to as bundles. Conclusions. Core formation in L1495/B213 has proceeded by hierarchical fragmentation. The cloud fragmented first into several pc-scale regions. Each of these regions later fragmented into velocity-coherent filaments of about 0.5 pc in length. Finally, a small number of these filaments fragmented quasi-statically and produced the individual dense cores we see today.