Dose-Dense MVAC With Pegfilgrastim Support in Subjects With Muscle-Invasive Urothelial Carcinoma

* Participants will be given a study infusion schedule for each treatment cycle. Each treatment cycle lasts three weeks. The infusion of methotrexate will take place on the first day of each cycle. Infusions of vinblastine, doxorubicin and cisplatin will take place on the second day and an injection of pegfilgrastim will be given on the third day. * During all treatment cycles participants will have a physical exam and will be asked questions about their general health and any problems they might be having and any medications they may be taking. * Following completion of study treatment, but before surgery, participants will have an assessment of their tumor by CT scan of the chest and and MRI of the abdomen and pelvis. * Following the participants surgery, we would like to keep track of their medical condition indefinitely, or until this study is officially completed. We would like to do this by calling the participants on the telephone once a year to see how they are doing.