  We establish direct connection between ghost-free formulations of
RG-invariant perturbation theory in the both Euclidean and Minkowskian regions.
By combining the trick of resummation of the $\pi^2$-terms for the invariant
QCD coupling and observables in the time-like region with fresh results on the
"analyticized" coupling $\alpha_{\rm an}(Q^2)$ and observables in the
space-like domain we formulate a self-consistent scheme, free of ghost
troubles. The basic point of this joint construction is the "dipole spectral
relation" emerging from axioms of local QFT. Then we consider the issue of the
heavy quark thresholds and devise a global scheme for the data analysis in the
whole accessible space-like and time-like domain with various numbers of active
quarks. Observables in both the regions are presented in a form of non-power
perturbation series with improved convergence properties. Preliminary estimates
indicate that this global scheme produces results a bit different - on a few
per cent level for $\bar{\alpha}_s$ - from the usual one, thus influencing the
total picture of the QCD parameters correlation.
