actually all these words are synonyms. but disturb - interrupt smth/smb, (emotianl state also) bother - to make (give) some problems or troubles to somebody annoy - usually used with strong emotional state

Hi Manuel - disturb, bother, and annoy are all synonyms, but in my opinion: "Do not disturb" - is a polite way of asking/telling "don't bother me" - firmly telling "that annoys me" = "that irritates me" ---> this is more intense and stronger than the other two. it's closer to almost being mad about something because it disturbs/bothers to a high degree. hope that helps.

Some other uses: "I'm sorry to bother you but [enter question here]." "Don't annoy me with your stupid music." "Oh, sorry, I didn't know you were studying. Did I disturb you?"