you cease to exist every time you fall asleep, but don't your cells or body exist?
"You" meaning your sense of self. The "self" is generally thought of as an entity, and some believe that when that entity goes to sleep it is no more. Upon waking up, the entity is born again, assembled from memories of the last entity. Each evening one "I" ends, and the next morning another "I" is born. All of them together give the overall perception of "you living your life". But what holds them together? Some kind of internal ability, or external influence?
"The day we're born is the day we start to die." So in your opinion we do die?
According to your definition of death, if there is life after the change, it was not death.