Quintom dark energy models with nearly flat potentials

We examine quintom dark energy models, produced by the combined consideration of a canonical and a phantom field, with nearly flat potentials and dark energy equation-of-state parameter w₃₄ close to -1. We find that all such models converge to a single expression for w₃₄ (z), depending only on the initial field values and their derivatives. We show that this quintom paradigm allows for a description of the transition through -1 in the near cosmological past. In addition, we provide the necessary conditions for the determination of the direction of the -1 crossing.