  (Abridged.) We present a thorough analysis of the current solar neutrino
data, in the context of two-flavor active neutrino oscillations. We aim at
performing an accurate and exhaustive statistical treatment of both the input
and the output information. Concerning the input, we analyze 81 observables,
including the Cl rate, the total Ga rate and its winter-summer difference, the
44 spectrum bins from SK and the 34 spectrum bins from SNO. We carefully
evaluate and propagate the effects of 31 correlated systematic uncertainties,
including 12 SSM input errors, the 8B neutrino energy spectrum uncertainty, as
well as 11 and 7 systematics in SK and SNO, respectively. Concerning the
output, we express the chi-squared analysis results in terms of ``pulls,''
embedding the single contributions to the total chi-squared. It is shown that
the pull method, as compared to the (numerically equivalent) covariance matrix
approach, is not only simpler and more advantageous, but also includes useful
indications about the preferred variations of the neutrino fluxes with respect
to their SSM predictions. Our results confirm the current best-fit solution
(LMA), but also allow, with acceptable statistical significance, other
solutions in the low-mass (LOW) or in the quasi-vacuum oscillation (QVO)
regime, while the small mixing angle (SMA) solution could be recovered only by
ad hoc ``recalibrations'' of several SSM and experimental systematics.
