System.Data.SQLite Not Supporting Multiple Transactions

Question

So I am having an interesting issue with System.Data.SQLite and using multiple transactions. Basically I have the following code which fails:

using (IDbConnection connection1 = new SQLiteConnection("connectionstring"), connection2 = new SQLiteConnection("connectionstring"))
{
    connection1.Open();
    connection2.Open();

    IDbTransaction transaction1 = connection1.BeginTransaction();
    IDbTransaction transaction2 = connection2.BeginTransaction();    // Fails!

    using(IDbCommand command = new SQLiteCommand())
    {
        command.Text = "CREATE TABLE artist(artistid int, artistname text);";
        command.CommandType = CommandType.Text;
        command.Connection = connection1;
        command.ExecuteNonQuery();
    }

    using (IDbCommand command = new SQLiteCommand())
    {
        command.Text = "CREATE TABLE track(trackid int, trackname text);";
        command.CommandType = CommandType.Text;
        command.Connection = connection2;                    
        command.ExecuteNonQuery();
    }

    transaction1.Commit();
    transaction2.Commit();

}

From what I've read it seems that System.Data.SQLite should support nested and by extension sequential transactions. The code fails on line 7 (where the second transaction is declared) with the following exception:

System.Data.SQLite.SQLiteException: The database file is locked

System.Data.SQLite.SQLite3.Step(SQLiteStatement stmt)
System.Data.SQLite.SQLiteDataReader.NextResult()
System.Data.SQLite.SQLiteDataReader..ctor(SQLiteCommand cmd, CommandBehavior behave)
System.Data.SQLite.SQLiteCommand.ExecuteReader(CommandBehavior behavior)
System.Data.SQLite.SQLiteCommand.ExecuteNonQuery()
System.Data.SQLite.SQLiteTransaction..ctor(SQLiteConnection connection, Boolean deferredLock)
System.Data.SQLite.SQLiteConnection.BeginDbTransaction(IsolationLevel isolationLevel)
System.Data.Common.DbConnection.System.Data.IDbConnection.BeginTransaction()

Does anyone know what the issue is or how to get around this? I feel having concurrent transactions is essential for any database system so there must be some way to do this.

Thanks!