Relativistic invariance of accelerations?

Is the acceleration invariant under change of reference frame?
We imagine an accelerated rocket (starting from rest to simplify).
We then set x=(1/2)a.Tr²
Which will result in x=(c²/a).[sqrt(1+a²To²/c²)-1]
But let's change the frame of reference and assume another frame of reference R'
which sees the distance AB in R move away over O'x' where M is in accelerated movement from A towards B.
Can we consider that in R' this acceleration is constant?
Doctor Hachel says no.
I would like to have the opinion on this from the excellent Python, for example.
R.H.