Dynamical algebras of general two-parametric Pöschl-Teller Hamiltonians

► A set of operators intertwining two-parametric Pöshl-Teller Hamiltonians is found. ► The explicit action of shift and ladder operator types is obtained. ► These operators generate a dynamical algebra that close a so(4,2) Lie algebra. ► A unitary irreducible representation of an associated realization is characterized.