  An analytic form for the conductivity tensor in crossover between two quantum
Hall plateaux is derived, which appears to be in good agreement with existing
experimental data. The derivation relies on an assumed symmetry between quantum
Hall states, a generalisation of the law of corresponding states from rational
filling factors to complex conductivity, which has a mathematical expression in
terms of an action of the modular group on the upper-half complex conductivity
plane. This symmetry implies universality in quantum Hall crossovers. The
assumption that the $\beta$-function for the complex conductivity is a complex
analytic function, together with some experimental constraints, results in an
analytic expression for the crossover, as a function of the external magnetic
field.
