VB.Net, use linq transaction to run s/p that contains transaction

I have some VB.Net code that runs several SQL stored procedures in sequence.  Table updates within each of the sprocs are wrapped in a transaction.  For example, sp1 starts a transaction, updates 5 tables, commits or rollsback.  It returns a success code to the calling program.  If successful, sp2 starts a transaction, updates 3 tables, commits or rollsback.  It returns a success code to the calling program.  If successful ... and so on.

I am using linq so I have:

dc.sp1(parameters,success)
If success = true then
    dc.sp2(parameters, success)
    if success = true then
        dc.sp3(parameters,success)
    end if
end if

and so on

What I want to do is start a transaction for dc and if success is false for ANY of the sprocs, roll everything back.

In other words, there will be transactions within the "dc transaction".  If the dc transaction is rolled back, will the nested transactions also be rolled back?