  This publication provides a coherent treatment for the reactor neutrino flux
uncertainties suppression, specially focussed on the latest $\theta_{13}$
measurement. The treatment starts with single detector in single reactor site,
most relevant for all reactor experiments beyond $\theta_{13}$. We demonstrate
there is no trivial error cancellation, thus the flux systematic error can
remain dominant even after the adoption of multi-detector configurations.
However, three mechanisms for flux error suppression have been identified and
calculated in the context of Double Chooz, Daya Bay and RENO sites. Our
analysis computes the error {\it suppression fraction} using simplified
scenarios to maximise relative comparison among experiments. We have validated
the only mechanism exploited so far by experiments to improve the precision of
the published $\theta_{13}$. The other two newly identified mechanisms could
lead to total error flux cancellation under specific conditions and are
expected to have major implications on the global $\theta_{13}$ knowledge
today. First, Double Chooz, in its final configuration, is the only experiment
benefiting from a negligible reactor flux error due to a $\sim$90\% geometrical
suppression. Second, Daya Bay and RENO could benefit from their partial
geometrical cancellation, yielding a potential $\sim$50\% error suppression,
thus significantly improving the global $\theta_{13}$ precision today. And
third, we illustrate the rationale behind further error suppression upon the
exploitation of the inter-reactor error correlations, so far neglected. So, our
publication is a key step forward in the context of high precision neutrino
reactor experiments providing insight on the suppression of their intrinsic
flux error uncertainty, thus affecting past and current experimental results,
as well as the design of future experiments.
