we introduce a cosmological frame which we call the river frame. In this frame, photons and any object can be thought as fishes swimming in the river and relations are easily expressed in either the metric or the covariant formalism then ensuring a transparent geometric meaning. We then show that the river frame is useful to make perturbative and non-perturbative analysis in cosmology. In particular, we use it to obtain the fully nonlinear generalization of the Sachs-Wolfe formula (which describes the CMB temperature anisotropies) and also use it to discuss second-order cosmological perturbations.