Motivation for using blank between all labels is not clear

[jotix16]

Since we can have an ϵ before or after any token in Y, it’s easier to describe the algorithm using a sequence which includes them. We’ll work with the sequence Z =[ϵ, y_1, ϵ, y_2, ..., ϵ, y_U, ϵ]

If seems like you are using blanks in between all output labels and at the beginning and end with the motivation that it is an example sequence which makes the algorithm easier to understand.

Isn't this the approach we use on all output sequences? It is kind of confusing to say that we put the blanks because it is easier to describe the algorithm.

Am I having a misconception somewhere?

Edit:
Link to the place in the post

[awni]

CTC assigns a score to the sequence Y = [y_1, y_2, ..., y_U], namely p(Y | X). This is different than the sequence Z with the blanks inserted. We just use Z to describe the algorithm but the blanks are optional.

[jotix16]

Here you say that alpha is the score of the subsequence Z and alpha is calculated assuming that exact Z as sequence. Wouldn't the calculation of alpha change if we would assume another Z sequence, for example using always 2 blanks in between each label?