  We study the effect of oxygen-doping on the critical temperature, Tc, the
vortex matter phase diagram and the nature of the coupling mechanism between
the Cu-O layers in the three-layer Bi2Sr2Ca2Cu3O10+delta (Bi-2223) compound.
Contrary to previous reports, in the overdoped (OD) regime we do find a
variation of Tc with increasing the oxygen partial-pressure of the
post-annealing treatment. This variation is less significant than in the
bi-layer parental compound Bi-2212 and does not follow the universal Tc
vs.delta relation. Magnetic measurements reveal that increasing delta enlarges
the field and temperature stability of the Bragg glass phase. These findings
imply that the interlayer coupling between Cu-O layers enhances with delta. The
anisotropy parameter estimated from directional first-penetration field
measurements monotonously decreases from 50 in the underdoped (UD) to 15 in the
OD regimes. However, the in-plane penetration depth presents a boomerang-like
behaviour with $\delta$, reaching its minimum value close to optimal doping.
These two facts lead to a crossover from a Josephson(OD) to
electromagnetic(UD)-dominated coupling of adjacent Cu-O layers in the vicinity
of optimal doping.
