I expect you want to merge changes from your_branch into my_branch? please update your question accordingly, it is not clear what you want to merge from where.
You need to have a checked out working copy to merge into. Also I expect it is your current directory as otherwise the merge command fails. However, it is not clear to which SVN branch this Workingcopy points so please state this as well. I expect this is my_branch in your case.
You performed a "2-URL merge" which is: showing you the difference between my_branch and your_branch and merge them into working copy (my_branch). In the result it will be the same as your_branch undoing all changes done on my_branch (my_branch+ [your_branch-my_branch] = your_branch).
What you usually want is a "complete merge". Just state the branch you want to merge from and the changes will be applied to your working copy:
svn merge http://repo.com/apps/service/branches/your_branch
This will show up all changes from your_branch in my_branch
To complete the list: the 3rd merge is "cherry-pick merge" and looks like "complete merge" but selects certain revisions to merge.