Why did the Irish get doors and we didn't?
Because they were built later than our native mark 3s; in 1985, following the mark 3B “Manchester Pullman” vehicles through works, by which point powered doors had been better developed for mark 3s. I’m sure that the mark 3B fleet could have been fitted with such a feature from new, but it makes more sense for them to have matched the rest of the indigenous mark 3 fleet.
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Was there much difference between mk2a and mk2b or mk2d and mk2e?
Compared to mark 2As, the mark 2B carriages had wider exterior doors wrapped round to the vehicle ends, a slightly longer body, no mid-carriage exterior door and one less toilet.
AFAIK, the only way mark 2Es differed from mark 2Ds was in having smaller toilets. The mark 2Fs differed again by having Intercity 70 seats, as fitted to the mark 3s, modified air con and different interior panelling.
As such, the scope of the changes being made to the Chiltern mark 3s, remembering that the alterations will be further reaching than simply fitting power doors to the outside, or so I've been led to believe, suggests to me that a mark 3C classification would be entirely appropriate.
I don’t know of their being that many differences between the mark 3A and mark 3B coaches either, beyond the difference in construction date of 7-9 years from the original mk 3A build: The mark 3B FOs, the former Manchester Pullman vehicles, are slightly heavier than their mark 3A equivalent, and were originally fitted with revised lighting and APT-style (Intercity 80?) seating. The three BFOs were of course a completely new design, but surely the construction methods were the same as the original build.