Many problems in analysis are described as weigthed norm inequalities thet have given rise to different classes of weights, such asAp- weights of Mukenhoupt, Bp-weights of Ario and Mukenhoupt, ect. Our purpose is to show that different classes of weigths are relaterd by mean of composition with classical transforms. Typical exemples are Ap-weights as indefinite integrals of Bp−1-weights, and Mp-weights (for which Hardy transform is bounded) as Hardy transforms of Bp- weights. We pay special atention to monotonic weights.