The sample sheet has "any" as the identifying name (rather than "value"). If on each sheet, these are all in the same column, this should do the job. The loop for looping through various sheets of nasty data is indicated.
Sub demo()
Dim sourceSheet As Worksheet
Dim destinationStart As Range
Set destinationStart = ThisWorkbook.Sheets(2).Range("a1")
Set destinationStart = destinationStart.Range("a1")
Range(destinationStart, destinationStart.Offset(0, 3)).EntireColumn.ClearContents
sourceSheet = ThisWorkbook.Sheets(1)
Rem begin loop through source sheets
Call moveAny(sourceSheet, destinationStart.EntireColumn.Range("a65536").End(xlUp))
Rem loop
End Sub
Sub moveAny(sourceSheet As Worksheet, destinationPlace As Range)
Dim foundCell As Range, baseSheet As Worksheet
Dim dataRange As Range
Dim oneArea As Range
Set baseSheet = ActiveSheet
With sourceSheet
.Activate
.AutoFilterMode = False
Set foundCell = Nothing
On Error Resume Next
Set foundCell = Cells.Find(What:="any", After:=.Range("a1"), LookIn:=xlValues, _
LookAt:=xlWhole, SearchOrder:=xlByRows, SearchDirection:=xlNext, MatchCase:=False)
On Error GoTo 0
If Not (foundCell Is Nothing) Then
Set dataRange = Range(foundCell, foundCell.Offset(0, 3)).EntireColumn
Set dataRange = Application.Intersect(.UsedRange, dataRange)
dataRange.AutoFilter Field:=1, Criteria1:="Any"
For Each oneArea In Application.Intersect(dataRange, .Cells.SpecialCells(xlCellTypeVisible)).Areas
oneArea.Copy Destination:=destinationPlace
Next oneArea
.AutoFilterMode = False
End If
End With
baseSheet.Activate
End Sub