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.
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