Does a tertiary carbocation rearrange to another tertiary carbocation?
Option B is the correct one. The process of dehydration of alcohols follow E1 elimination mechanism which involves two steps out of which the first one is slow ionisation of C-X bond( where X is any hetro atom) and the second step is  fast removal of $H^+$ ion .Since the first step is slow it provides enough time for the carbocation to rearrange and form a stable carbocation . The mechanism itself is self explanatory. Firstly as Oxygen possess lone pairs of electrons so the $H^+$ ion attacks the OH group as a result the $H_2O $ molecular gets eliminated resulting in a positive charge there.  Now hydride shift takes place as the so formed $ \textbf{Carbocation is more stable as it has 7 alpha hydrogens compared to the 5 alpha hydrogens of the previous carbocation}$. Now the C-C bond undergoes ionisation to form a three degree Carbocation and a carbanion . Now this carbanion forms a bond with the Carbocation formed earlier to form a six member ring . Now the resulting carbocation undergoes methyl shift which produces more stable three degree Carbocation. Now a $H^+$ ion from the neighbouring carbon atom is ejected as a result the pie bond is formed.