Abstract: In permissionless blockchains, transaction issuers include a fee to incentivize miners to include their transaction. To accurately estimate this prioritization fee for a transaction, transaction issuers (or blockchain participants, more generally) rely on two fundamental notions of transparency, namely contention and prioritization transparency. Contention transparency implies that participants are aware of every pending transaction that will contend with a given transaction for inclusion. Prioritization transparency states that the participants are aware of the transaction or prioritization fees paid by every such contending transaction. Neither of these notions of transparency holds well today. Private relay networks, for instance, allow users to send transactions privately to miners. Besides, users can offer fees to miners via either direct transfers to miners' wallets or off-chain payments -- neither of which are public. In this work, we characterize the lack of contention and prioritization transparency in Bitcoin and Ethereum resulting from such practices. We show that private relay networks are widely used and private transactions are quite prevalent. We show that the lack of transparency facilitates miners to collude and overcharge users who may use these private relay networks despite them offering little to no guarantees on transaction prioritization. The lack of these transparencies in blockchains has crucial implications for transaction issuers as well as the stability of blockchains. Finally, we make our data sets and scripts publicly available.