You could outfactor(?) the combined ifs:

If NAME =~ /BAA/
   if ITEMS_A =~ /^134/
     if ITEMS_B =~ /^134/ THEN
       TBAA+=SUM
       a++;
     elsif ITEMS_B !~ /^(134|00)/ THEN
       OBAA+=SUM
       b++; 
     elsif ITEMS_B =~ /^00/ THEN
       IBAA+=SUM
       ab++; 
     else
       EBAA+=SUM
       c++;
       # AFAICS this will never be reached.
       # Either ITEMS_B starts wit 134 or 00 or something
       # else. The last case is targeted by your second
       # ITEMS_B-if
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To shorten it, or at least make it more switch-like, in perl you could use the aliasing to $_ or "for":

SWITCH: for ($ITEMS_B) {
  /^134/ && do {
      # see above
      last SWITCH;
    };
  !/^(134|00)/ && do {
      # see above
      last SWITCH;
    };
  /^00/ && do {
      # see above
      last SWITCH;
    };
  # else
  do {
    #see above
    last SWITCH;
  }
}
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