We study how changing the interaction strength between the chain qubits allows us to obtain perfect or pretty good state transfer and present explicit analytic expressions for their transmission fidelity. For particular values of the interactions between the qubits, transmon chains are equivalent to generalized SSH chains and show the traditional traits observed in chains with topological states, localized states at the extremes of the chain, and eigenvalues that lie inside the spectral gap. Consequently, we study the quantum state transfer on chains with dimerized interactions, looking for chains with fast transfer times. We show that, in many cases, asking for fast transfer times results in chains with dimerized interactions that do not have topological states.