The phase behavior and linear viscoelasticity of a mixture of a matched diblock and triblock copolymer of styrene and ethylene-butene-1 are reported. The mixture undergoes reversible thermotropic transitions from a cylindrically ordered state at low temperatures to a spherically ordered state at intermediate temperatures to a disordered state at high temperatures. The morphological assignments were based on TEM and SANS measurements, which also revealed a decrease in the domain size in the spherically ordered state as compared to the cylindrically ordered state. The kinetics of the order-order transition are extremely slow, with the sample exhibiting rheological characteristics similar to a disordered material immediately after heating from the cylindrical to the spherical state. The transition exhibits a long induction period wherein the sample continues to behave like a disordered material followed by a rapid increase in the storage modulus and a final plateau value. The kinetics and rheological characteristics of a material quenched ti om the disordered state to the spherical state are remarkably similar to those obtained after heating from the cylindrical to the spherical state, suggesting that the transition from cylindrically ordered to spherically ordered microdomains proceeds via a mesoscopically disordered state.