Hi,
How to see transactions that occured in the off-chain part ?
I understand LN will register finally the balances on the blockchain, but what about all the small transactions during the off-chain process ?
Will there be a blockchain.info like tool to explore all transactions ?
No because the transactions in Lightning are not broadcast publicly. They are encrypted and sent through the network from the sender to the receiver.
Blockchain should be transparent and be able to register all transactions. If LN allows off-chain small transactions for performance purpose, fine, but how to ensure transparency ?
I disagree with this. Bitcoin should be private and fungible, and Lightning offers significant privacy improvements. It is a plus.
I might not understand well the final process of registration of the balance sheet on the blockchchain, will it show all transactions between Alice and Bob ?
So many questions

Thanks all.
Think of Lightning as going to a bar. You go to the bartender and open a tab. When the bar closes you settle your tab and leave.