I have not personally billed OB/GYN however, here is some information:
Global maternity care includes: "pregnancy-related antepartum care, admission to Labor and Delivery, management of labor including fetal monitoring, delivery, and uncomplicated postpartum care until six weeks postpartum"
Services not included in global maternity care: "laboratory tests (excluding dipstick urinalysis), diagnostic ultrasound, amniocentesis, cordocentesis, chorionic villus sampling, fetal stress test, and fetal non-stress test"
If the same provider renders all services then it should be billed as global maternity care. I do not believe you need a "log" but obviously all care provided would/should be documented in the patient's chart which would technically be logging all services.
I hope that is helpful!