Try something in this manner...
#!/usr/bin/perl
use strict;
my @file = do { local $/ = ">"; <DATA> };
print map { "$_\n" } @file;
__DATA__
>i:/13414 Ccl9 (88)/sequencing/13414_fasta.Contig1
TTTCTCCGGCCCCCTCCTCCCGCGGGGGAAAAAACCCGGGGAGCAGTCGG
GCAGGGGTTTTTTGGTTTTTTCAAAATAAAAAGGGGTGCCCGTTGGGGGGcd
GGGGGGGTGCAGGTTTCAACCCCCCCCCCCAAAGAAAAAAAAATTTTGGG
GAATTTTTGGGGGGCTCCACCAGTTTTCGGGGTTTTTGGGCCTTTTCAGA
AGGTAGGTTGGACGCGGATTGGGCAATAAACCACCCCGCTTCATCGGATA
ATTTTCCCCGGCCGAAAAGGGCCGCGGGGCCGGTGGGCGGCCTTGGGTTT
>i:/13414 Ccl9 (88)/sequencing/13414_fasta.Contig2
TAAACCCAAGGCCCCCCAGGTAAAAAAAAAACCGGCCAGGGGGGGGGGGG
TAAAAAAAACCAAGTGTCACCCAGGGTGGAGATCCCCGGAAAAGGAAAAG
GGGGGTTTTTTATTCGAAACGGGGAAAACTTTCACAAAATTTTGGAAGAA
TCCCCTTTAATGTTTTCTTTTCAAAAGGGGGTAAAAAAACCACCTTTAAA
AAGAAGTCTACCTTGGGAAAAAATAATTTTTGGGAAAATTTAAAAATTGA