Manage Trash So

Retina, 25

i+`(\w)(.*,.*)\1
$2
^\W*$

Try it Online! Additionally, you can run a modified multi-line version.

Delete letters from before the comma along with their matches after the comma. If we have no letters left then it was an anagram.

05AB1E, 9 8 bytes

Code:

lvyð-{}Q

Explanation:

l         # Lowercase the strings
 vy   }   # Map over the list, for each...
   ð-     #   remove spaces
     {    #   and sort
       Q  # Check equality

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Pyth, 11 10 bytes

Thanks to @FryAmTheEggman for teaching me the power of ;!

qFmSr-d;0Q

Try it here!

Takes a list of two strings as input.

Explanation

qFmSr-d;0Q    # Q = input

  m      Q    # map Q with d as lambda variable
     -d;      # filter spaces out of the string
    r   0     # convert to lowercase
   S          # sort all characters in string
qF            # Unfold resulting list and check for equality