ISSUE:

Hello.
I need to come up with a mechanism for that reaction.

Hello Valen, the problem you propose is solved in the following way:

Thank you so much.
Could you explain to me what happens in the reaction for the spiro to become a bicycle, please.

It is a transposition of the carbocation generated after leaving the water, it is transposed from a tertiary carbocation to a secondary one, releasing the angular tension of the spirocycle

An alcohol treated with concentrated or fuming sulfuric acid produces its dehydration, giving rise to an alkene. Since it is a tertiary alcohol, the reaction takes place through an E1 mechanism, that is, protonation of the leaving group and its subsequent exit, then It takes place through carbocation, as we already know, carbocations are susceptible to rearrangement as long as they reach greater stability, in this case, it is the carbocation rearrangement by ring expansion, which explains why the tertiary carbon evolves to one Secondary, due to the tension that is released and the stability that a six-membered cycle supposes, as another forum member perviously commented to me.

An apology, sometimes due to lack of time or consideration my explanations tend to be somewhat hasty and perhaps far from the detail that is sought so here it goes again.
The first step is the protonation of the alcohol, this is carried out when an unbonded lone pair interacts with a hydrogen from sulfuric acid, this reaction can be classified as a Brönsted Acid-Base reaction. Subsequently, a dissociation takes place, breaking the link CO, heterolytically in favor of oxygen, leaving carbon with a fewer pair of electrons, and therefore a positive charge, this species is known as a carbocation, remember that these species will be formed based on their stability, in this case it is a tertiary carbocation, however it is found in a spirocyclic system, which is highly stressed by the bond angles between the carbons and hydrogens present in the structure.
Subsequently, that carbocation is rearranged, this is carried out through a transition state, that is, the exact point where a bond is broken, between the carbons. ab and the bond between the carbons bc it forms. This rearrangement has made carbon c recover the pair of electrons that it was missing when forming a new bond, in this way it returns to being neutral while carbon to it has lost a pair of electrons, causing it to now have a positive charge, i.e., roughly speaking, the carbocation has transposed from carbon c to carbon to.
The new carbocation promotes a removal of a hydrogen from the adjacent carbon, resulting in the final product.