For prerequisites for the DM program, Standards state the following:
Diver Prerequisites:
"Certified as a PADI Advanced Open Water Diver and PADI Rescue Diver"
Standards also state that for continuing education courses that have PADI, DSAT or EFR certification prerequisites, the Instructor may accept divers with certifications through other training organizations into a PADI course using the general guideline, and after conducting a knowledge and skill preassessment.
Equivalents to the above DM prerequisites would be:
PADI Advanced Open Water Diver — proof of certification beyond entry-level (at least two certifications total); proof of 20 or more logged dives; documented experience in deep diving and underwater navigation.
PADI Rescue Diver — proof of certification in diving rescue.
EFR Primary Care — proof of current CPR training.
EFR Secondary Care — proof of current first aid training.
So, your certifications may qualify, however it will be up to the individual Instructor to decide.