According to my Lippincott nursing drug book, Phenytoin (Dilantin) may decrease the effect of the steroid when used together. Therefore the steroid dosage would be adjusted according to what your physician prescribes. It does also state that prednisone is used cautiously in patients with history or seizures. There is nothing specific about those anticonvulsant med levels being affected. But I'm sure your physician will be monitoring you carefully.
I think the best person to ask this question to would be your pharmacist. They are typically very knowledgeable about how medications interact with one another. Normally, when you get you rscripts filled (so long as you're using the same pharmacy for all of them), their computers will automatically check for interactions, but if you're just doing research on the possible interactions (or use different pharmacies), just give them a call. I've always found pharmacists to be not only very knowledgeable, but also very willing to answer any and all questions about your meds.
Best of luck! I've been through a liver biopsy myself and it's no fun!