There are three issues of Magna Carta in the  collections of durham cathedral

The exemplifications of Magna Carta at Durham comprise the issue of November 1216, the issue of 11 February 1225, and the issue of 28 March 1300.

The Cathedral also possesses three issues of the Forest Charter composed in 1217 to protect the rights of those who dwelt within the royal forest.The Forest Charters are the issues of 1217, 1225 and 1300. The 1217 Forest Charter is one of only two surviving copies.

The earliest of the Durham Cathedral copies of Magna Carta, the November 1216 Bristol exemplar, is the only known copy of this issue to survive. It contains 42 clauses (as compared to the 61 of the 1215 issue). 

The 1225 issue of the Magna Carta held at Durham Cathedral is one of four surviving exemplars. Issued when Henry III reached the age of majority, it is a shorter version (37 articles), a concession of liberties in return for a fifteenth part of moveable goods. It includes the new statement that the charter was issued spontaneously and of the King’s own free will. This was the first version of the charter to enter English law. The Durham copy is in a neat chancery-style hand. The accompanying 1225 Forest Charter at Durham is one of three surviving copies.

The final Magna Carta at Durham is the issue of 28 March 1300 (DUL DCD 2.2.Reg.2), the last full exemplification. It is in excellent condition, a marginal hole not affecting the text, the best of the six surviving copies.  

The March 1300 Forest Charter (DUL DCD 2.2.Reg.8), one of two copies, is also in excellent condition with a decorated E similar to that of the Durham Magna Carta of 1300.

It is not clear why there are three versions of Magna Carta at Durham Cathedral, but it is likely that issues of Magna Carta were distributed around the country to ensure people heard about the contents, perhaps particularly important for the people of the palatinate of Durham. The charters might well have been proclaimed from the pulpit and then retained in the Cathedral’s archive.
Durham Cathedral’s archive is particularly well-preserved and, where other places may have disposed of the previous issue of Magna Carta when they received a new version, Durham seemingly did not. The charters have probably always been at Durham as the monks were certainly making copies of the 1225 Magna Carta and the Forest Charter into a book (cartulary) in the archive not long after they were issued and they have references on the back of them indicating that the monks had also catalogued them at around that time.
It is also worth noting that three of the surviving 1215 originals come from cathedrals. The provenance of the fourth has never been established, but could well be somewhere like St Paul's.  This suggests that the bishops were responsible for the distribution and custody of the charter, a suggestion that makes sense given that the sheriffs were the object of enquiry under the charter and could not therefore, as would normally have been the case, be entrusted with the charter's publication.