Yes, these are all equivalent. Most important however is that the concept needs to be man hours and not man days. A man hour is the amount of work an average person can perform in an hour without a break.
A man day is a bit nebulous as people cannot work 24 hours. Large projects do use man days and man years. A man day then needs to have some understanding of how many hours per day as assumed.
A man year is even more nebulous and rooted in culture and custom. Reported highs and lows for hours worked per year vary from about 1,400 to 2,400.