A transaction log backup is a record of the database changes that have occurred since the last transaction log backup. SnapManager supports transaction log backups in order to provide a more granular level of database backup and to recover the transactions committed since the most recent full backup.
SnapManager creates a backup of a transaction log by copying transaction log data to a file in the SnapInfo directory. Transaction log backup files are named using the following convention:
Every record in the SQL Server transaction log is uniquely identified by a log sequence number (LSN). LSNs are ordered such that if LSN2 is greater than LSN1, the change described by the log record referred to by LSN2 occurred after the change described by the log record LSN.
So, as far as i know if yiu have the same LSN means that there weren't any changes in the database