We calculate transformation pathways between fullerene and octahedral carbon clusters and between a buckyball and its bowl-shaped isomer. The energies and gradients are provided by efficient tight-binding potentials, which are interfaced to our Energy Landscape exploration software. From the global energy landscape, we extract the mechanistic and kinetic parameters as a function of temperature, and compare our results to selected density functional theory (DFT) (PBE/cc-pVTZ) benchmarks. Infrared spectra are calculated to provide data for experimental identification of the clusters and differentiation of their isomers. Our results suggest that the formation of buckyballs from a buckybowl will be suppressed at elevated temperatures (above around 5250 K) due to entropic effects, which may provide useful insight into the detection of cosmic fullerenes.