I assume you are referring to a home installation, as it would be a somewhat different answer if this was in an industrial situation.
I believe you will find that neutral and ground are not bonded within the generator, therefore the 4 lines. The only place it should be bonded is at the Main Service Panel. The neutral is a current carrying conductor, ground is not! Lets say you have a high load (or short) that the Main panel sees. The neutral potential to ground can be as high as the Main voltage (120V or 220V)! If it were bonded at the generator and you were touching it at that instant, you're dead!
The ground is never switched by the transfer switch, only the main conductors (& sometimes neutral). I suggest you check the NEC and local codes before you proceed. Also do not bond neutral and ground at the transfer panel, or any sub panels!
This link shows the transfer switch wiring. It also says that some Transfer switches do not switch the neutral leg. Yours is three pole so it would.
EDIT: Please read Since yours has bonding at the Gen, and you are switching the neutral you're okay. This article expresses the same concerns I listed above.