  We find exact relations among the sphere partition functions of
three-dimensional $\mathcal{N}=4$ superconformal Chern-Simons theories with
circular quiver diagrams. These relations suggest new dualities in gauge
theories which are the products of circular quiver gauge theories and decoupled
linear quiver gauge theories. The dualities can be interpreted as simple brane
transitions in the Hanany-Witten brane construction in type IIB string theory.
Interestingly, the brane transitions cannot be generated by the Hanany-Witten
transition or the ${\rm SL}\left(2,\mathbb{Z}\right)$ transformation. Our
results can be regarded as generalization and clarification of dualities
implied from Weyl symmetries of quantum curves. To obtain the exact results, we
employ the supersymmetric localization technique and the Fermi gas approach.
