In a recent composition of mine (for piano), I opted for several changes of tempo and key. Therefore, I use different Key Signatures. For example, from F Major + change to E Major+, then changing to G Major+ and finally arriving at Bb Major+.
It is not difficult because in the case of F Major $\rightarrow$ E Major, it is enough to just add the 4 SHARPS.
My doubt is this: the Bb specified in the key signature at the beginning (F Major), must I cancel it with a natural sign and then write the 4 sharps, or do I only put the 4 sharps?
How exactly are Key Signature changes made? I haven't found anything about this on Google.
As far as I know, when moving from a key with sharps to one with flats (or vice versa), it is common practice to put natural signs where the alterations were previously in the key signature, therefore writing the new ones. The same applies if moving from one key to another with a smaller number of sharps (or flats). For example, from A major to B-flat major, the key signature will be written as B-flat - E-flat - A natural - D natural.