Maybe to summarize and clarify what has been said.
The S&W .44 Magnum began shipping in January 1956 (one shipped in December 1955, but we won't count that one)
September 1956, the change order to eliminate the top sideplate screw issued.
June 1957, the change order to model mark the guns issued, the .44 Magnum to be the Model 29.
During the transition period between September 1956 until apparently early 1958, .44 Magnums were shipped with 5 screws and 4 screws, non model marked. It took awhile to make the changes as S&W used the frames already made before using the 4 screw ones. (I have a 4 screw non model marked .44 Magnum shipped in 1958)
The cylinder stop plunger and screw were eliminated in 1959, and the gun became the 3 screw model.
In 1960, the extractor rod threads were changed from right hand to left hand, the change resulted in the Model 29-2.
The 29-2 stayed the same for about 20 years or so, when the pinned and recessed were removed resulting in the 29-3. Again there was a transition period when there were 29-3s shipped with either pinned and not recessed, or recessed and not pinned. Maybe a few 29-2s were shipped that way too? Generally by 1982 they were pretty much 29-3s.