VB.NETでListに追加したインスタンス同士をリンク(同期)させたい

Public Class Class1
    Implements IDisposable

    '自分のインスタンスを保持しているListを記憶させるList
    Private _ListParent As New List(Of List(Of Class1))

    Public Sub New(name As String)
        Me.Name = name
    End Sub

    Public Property Name As String
        Get
            Return _Name
        End Get
        Set(value As String)
            If _Name <> value Then
                _Name = value
                If value Is Nothing Then
                    Dispose() 'NameがNothingになったら解放
                End If
            End If
        End Set
    End Property
    Private _Name As String

    Public Sub AddToList(list As List(Of Class1))
        'Listに自身を追加するついでに、追加したListを記憶
        list.Add(Me)
        _ListParent.Add(list)
    End Sub

    Public Sub Dispose() Implements IDisposable.Dispose
        If _ListParent Is Nothing Then
            Return
        End If

        '自身のインスタンスを記憶した全てのListから削除
        For Each list In _ListParent
            list.Remove(Me)
        Next
        _ListParent = Nothing
    End Sub

End Class

Public Class Test
    Private List1 As New List(Of Class1)
    Private List2 As New List(Of Class1)

    Public Sub Run()

        Dim test1 As New Class1("test1")
        Dim test2 As New Class1("test2")
        Dim test3 As New Class1("test3")

        'List1に要素を追加
        test1.AddToList(List1)
        test2.AddToList(List1)

        'List2に要素を追加
        test2.AddToList(List2)
        test3.AddToList(List2)

        test2.Name = Nothing

        Console.WriteLine(List2(0).Name) 'test3
    End Sub

End Class

Public Class Program

    Shared Sub Main()
        Dim test = New Test
        test.Run()
    End Sub

End Class