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- relativistic relative velocity composition law solely in terms of relative velocities?

I'm trying to understand this paper (equation 2.16 specifically):

Bini, D., Carini, P., & Jantzen, R. T. (1995). Relative observer kinematics in general relativity. Classical and Quantum Gravity. Am I correct in reading there is no way to express the relativistic relative velocity composition law solely in terms of relative velocities? I don't think the relative boost map ##B(u,u')## can be expressed as some formula of relative velocities? At the same time I find it highly counterintuitive that special relativity would force us to use the four velocities ## u## and ## u'## as part of the composition law.

Bini, D., Carini, P., & Jantzen, R. T. (1995). Relative observer kinematics in general relativity. Classical and Quantum Gravity. Am I correct in reading there is no way to express the relativistic relative velocity composition law solely in terms of relative velocities? I don't think the relative boost map ##B(u,u')## can be expressed as some formula of relative velocities? At the same time I find it highly counterintuitive that special relativity would force us to use the four velocities ## u## and ## u'## as part of the composition law.