Can can I identify my deposits to a wallet on a BTC (or LTC) blockchain (using the blockcypher api)
An old post, but why not. 
1st, the example address is MDUsWPcdJ2onP9bU5xxzdygqL1R51aAvva. It has 31 total transactions: 
https://longhorn.bullpay.com/?gateway=6&amp;data=MDUsWPcdJ2onP9bU5xxzdygqL1R51aAvva

The first transaction is this one:
https://longhorn.bullpay.com/?gateway=6&amp;data=b9ed3bbf129307b0a36fbb723e3a11d40959b4e109c01983a8ee2f0589cf52e5+

45 LTC was taken from the given address and bundled with 16 other inputs. 48 LTC was snet to LSd8c9iv8JuyFbi3ejEAdpqPcdRyhsiF4H and the remaining .02873313 LTC was returned to the MDU address.

What you are likely seeing here is change. To send that 48 from MDU it had to bundle together enough to cover the 48 along with the ~0.68 fee. The remainder was returned to MDU as change.

In your second example, 
https://longhorn.bullpay.com/?gateway=6&amp;data=2440d14ba777ac204b332f2e2043f415cb0d10670b4ca4f4b38284d3c8bbf9ef+

This transaction took multiple inputs from the MDU address along with a few others to cover what looks like the Lgam transaction of 10.7 LTC. This seems like a sloppy way of handling the inputs as the change resulted in more than one of the MDU inputs. Seems like juggling the inputs for no reason only to have it come back to the same address. Waste of gas in my opinion. The 3.09299- MDU input could have been dropped completely and this transaction would have still been fine.

I could go through the remainder but at this point i'd prefer more information. 


Which exchange are you using?
What does the exchange say are you deposits/withdrawals (line by line)?
What is your actual exchange "deposit" address?


I'm not sure you want to tell me exactly what your wallet is, if it is indeed this one. Ultimately exchanges in most cases don't let you "own" your wallet. You don't have the private key to it, it's shared among many other accounts. You "own" the number next to "LTC" and they juggle everything else as they see fit.