On the importance of textual criticism in synoptic studies: the case of ευθυς.
Back to ευθυς.
In the Westcott-Hort text and the Moulton-Geden concordance:
Matthew uses ευθεως 10  times 4.20, 22, 8.3, 13.5, [14.22], 31, 20.34, 24.29, 25.15, 26.49, 27.48.
Matthew also uses ευθυς 7 times 3.16, 13.20, 21, 14.27, 21.2, 3, 26.74.
Mark never uses ευθεως.
Mark uses ευθυς 40  times 1.10, 12, 18, 20, 21, 23, 28, 29, 30, 42, 43, 2.8, 12, 3.6, 4.5, 15, 16, 17, 29, [5.2], 29, 30, 42, 42, 6.25, 27, 45, 50, 54, 7.25, 8.10, 9.15, 20, 24, 10.52, 11.2, 3, 14.43, 45, 72, 15.1.
Obviously, ευθυς is a Marcanism.
More provacatively diagnostic, all seven of the ευθυς examples in Matthew are parallel to verses in Mark. Not only that, they are very tightly congruent in the rest of the Greek wording in their respective verses and they occur in both the narrative framework and in the words of Jesus. There is a literary connection. (Logically, either Matthew used Mark, Mark used Matthew, or both used a shared source.)
Since ευθυς is a Marcanism, the probable conclusion is that Matthew has borrowed seven examples of ευθυς from Mark, but himself prefers ευθεως. [NB: of the 11 ευθεως in Matthew, only 7 out of 11 Matthean ευθεως have an 'immediately' parallel in Mark. [[Mt 4.20, 4.22, 8.3, 13.5, 14.22, 20.34, 26.49]] If Mark were converting all 'immediately's in Matthew to ευθυς, it would be surprising that he only gets less than 2/3 of the ευθεως but 100% of the ευθυς.]
So what's the point of all the above?
Let's look at the Byzantine text.
In 46 variation units of ευθεως/ευθυς in Mark (Alex. has unique examples at 1.23, 5.42b, 7.25, 14.72, Byz at 1.31, 5.36, 7.35 [NA bracketed]):
the Byzantine text has ευθεως 40 times and ευθυς 2 [1.12, and 1.28].
The Byzantine-Alexandrian text agree to have either ευθεως or ευθυς 39  times.
Neither of the examples of ευθυς in Byz Mark have an ευθυς in Matthew! Byz Mark 1.12 is parallel to a Matthean τοτε, a distinctive Mattheanism that is not picked up in Mark anywhere. Byz Mark 1.28 is 'Marcan material' that has no equivalent in Matthew [Byz or Alex].
In the Byzantine text, Mark could have a source that has ευθυς since ευθυς is not a Marcan stylistic feature and Mark cannot borrow from Matthew's τοτε at Mark 1.12. Mark could be the copier of an unknown source. He would only have ευθυς where his source would have ευθυς, otherwise he continues with his personal ευθεως. The source, of course, could have many more ευθυς, three of which turn up in Byzantine Matthew [3.16 // ByzMark 1.9 ευθεως, 13.20//Byz Mark ευθεως, 13.21//Byz Mark ευθεως]. Byzantine Matthew, however, is not copying Mark but a shared source. Or else both Byzantine Matthew and Byzantine Mark infrequently and randomly add ευθυς. [Mt 3xx out of 18, Mk 2xx out of 42, never parallel.]
Or, in the Byzantine text one could argue that two ευθυς from an Alexandrian redaction/spelling of Mark have entered the Byzantine tradition at an early stage. This would leave unexplained the manner in which the ευθυς examples entered the Byzantine Matthean tradition on the assumption that the Byzantine text was original. There would not have been many Matthean ευθυς in an early Alexandrian redaction for penetrating Byz Matthew. Even though Byz Mark could be penetrated by Alex Mark in two places, it would be less likely that Byz Matthew would pick up three ευθυς from an Alex Matthew that only had 5 anyway. So Byz Matthew would become an infrequent and random user of ευθυς. One could say the same for Mark and have either Matthew or Mark ignore the others, as dicted by one's synoptic theory. Only one would need to be an 'ignorer' in order to explain the data and neither is a strong friend of ευθυς.
What is remarkable, is that regarding ευθυς/ευθεως in the Byzantine text the literary flow Mark to Matthew does not exist. Yet the Alexandrian text has a clear literary flow from Mark to Matthew on this point. Alexandrians can point to ευθυς as evidence that Matthew used Mark. But that datum is only as strong as the textual theory.