Theory - DH parameters of spherical wrist

Hello robot experts. I’m learning the foundations of robotics and this is mostly coordinate frames, Euclidean space, transformation matrices etc.
One especially interested topic is making a transformation matrix, by first choosing Denavit-Hartenberg parameters. I have a difficult time following one example in the book I’m using and this is an example of determining DH parameters for spherical wrist.
I have uploaded this screenshot. I know that since the joints are revolute, variables are angles theta. What I have trouble understanding is why not theta4 - pi/2, theta5-pi/2 and theta6+pi/2 instead of theta4, theta5 and theta6?
If the manipulator is in the home/zero position, than, it is obvious there is a 90 degrees (pi/2) angle between x3 and x4. The same is with x4 and x5 and x5 and x6. This choice of x axes is already done in the book. If I use theta-pi/2 instead of theta, of course I get different transformation matrix. Is this an error in the book, or since theta is variable and pi/2 a constant, sum: theta+pi/2 is also a variable, so it doesn’t matter.

I hope you understand my question.
Thank you for your help.