  In this work we present a closed form expression for Polyakov blocks in
Mellin space for arbitrary spin and scaling dimensions. We provide a
prescription to fix the contact term ambiguity uniquely by reducing the problem
to that of fixing the contact term ambiguity at the level of cyclic exchange
amplitudes -- defining cyclic Polyakov blocks -- in terms of which any fully
crossing symmetric correlator can be decomposed. We also give another,
equivalent, prescription which does not rely on a decomposition into cyclic
amplitudes and we underline the relation between cyclic amplitudes and
dispersion relations in Mellin space. We extract the OPE data of double-twist
operators in the direct channel expansion of the cyclic Polyakov blocks using
and extending the analysis of \cite{Sleight:2018epi,Sleight:2018ryu} to include
contributions that are non-analytic in spin. The relation between cyclic
Polyakov blocks and analytic Bootstrap functionals is underlined.
