While block.one will not be involved in any way in the transferability of the EOS Tokens, EOS Tokens could be transferred on a peer-to-peer basis or on platforms operated by 3rd parties during the EOS Token distribution period.
Remember! EOS Tokens will become fixed (non-transferable) on the Ethereum blockchain within 23 hours after the end of the final EOS Token distribution period which will occur on June 1, 2018 at 22:59:59 UTC.
Therefore, if you do not want to lose your EOS tokens, you should register your ETH wallet, containing the ERC20 EOS tokens, on the EOS blockchain before June 1. After that you will be able to transfer your ERC20 EOS tokens on the EOS blockchain.
You can also withdraw tokens to the exchange, where the transfer will happen automatically without interrupting trading.