Are there different factors for access concentration depending on which jhana an individual is entering?

I have heard that a practitioner does not go from first jhana directly to second jhana or from second jhana directly to third jhana and so on. Instead, they go through momentary and access concentration to get to first jhana; then they drop out of first jhana and go through momentary and access concentration to get to second jhana and so on. First of all, is this correct, am I totally wrong or is there debate with regards to this? Secondly, do the factors of access concentration change depending on which jhana someone is trying to enter?